Gravitational Collapse

We construct in the context of the AdS/CFT correspondence degenerate composite operators in the conformal field theory that are holographically dual to degenerate stars in anti de Sitter space. We calculate the effect of the gravitational back-reaction using the Tolman-Oppenheimer-Volkoff equations, and determine the "Chandrasekhar limit" beyond which the star undergoes gravitational collapse towards a black hole.

Warp drives are very interesting configurations in general relativity: At least theoretically, they provide a way to travel at superluminal speeds, albeit at the cost of requiring exotic matter to exist as solutions of Einstein's equations. However, even if one succeeded in providing the necessary exotic matter to build them, it would still be necessary to check whether they would survive to the switching on of quantum effects. Semiclassical corrections to warp-drive geometries have been analyzed only for eternal warp-drive bubbles traveling at fixed superluminal speeds. Here, we investigate the more realistic case in which a superluminal warp drive is created out of an initially flat spacetime. First of all we analyze the causal structure of eternal and dynamical warp-drive spacetimes. Then we pass to the analysis of the renormalized stress-energy tensor (RSET) of a quantum field in these geometries. While the behavior of the RSET in these geometries has close similarities to that in the geometries associated with gravitational collapse, it shows dramatic differences too. On one side, an observer located at the center of a superluminal warp-drive bubble would generically experience a thermal flux of Hawking particles. On the other side, such Hawking flux will be generically extremely high if the exotic matter supporting the warp drive has its origin in a quantum field satisfying some form of quantum inequalities. Most of all, we find that the RSET will exponentially grow in time close to, and on, the front wall of the superluminal bubble. Consequently, one is led to conclude that the warp-drive geometries are unstable against semiclassical backreaction.

Dark-matter (DM) halos are the scaffolding around which galaxies and clusters are built. They form when the gravitational instability of primordial density fluctuations causes regions which are denser than average to slow their cosmic expansion, recollapse, and virialize. Understanding the equilibrium structure of these halos is thus a prerequisite for understanding galaxy and cluster formation. Numerical N-body simulations of structure formation from Gaussian-random-noise initial conditions in the Cold Dark Matter (CDM) universe find a universal internal structure for halos. Objects as different in size and mass as dwarf spheroidal galaxies and galaxy clusters are predicted to have halos with the same basic structure when properly rescaled, independent of halo mass, of the shape of the power spectrum of primordial density fluctuations, and of the cosmological background parameters. This remarkable universality is a fundamental prediction of the CDM model, but our knowledge is limited to the "empirical" N-body simulation results, with little analytical understanding. We summarize here our attempts to fill this gap, in an effort to derive and give physical insight to the numerical results and extend them beyond the range of numerical simulation: (1) Simulated halos which form from highly simplified initial conditions involving gravitational instability in a cosmological pancake show that many of the universal properties of CDM halos are generic to cosmological gravitational collapse and do not require Gaussian-random-noise density fluctuations or hierarchical clustering. (2) A fluid approximation derived from the Boltzmann equation yields an analytical theory of halo dynamics which can explain many of the N-body results if the complex mass assembly history of individual halos is approximated by continuous spherical infall. The universal mass growth history reported for CDM N-body halos corresponds to a time-varying infall rate which self-consistently determines the shape of the equilibrium halo profile and its evolution without regard for the complicated details of the merger process.

Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological applications. The conditions imposed in addition to spherical symmetry turn out to take a simple form at the kinematical level of loop quantum gravity, which allows a discussion of their implications at the quantum level. Moreover, the spherically symmetric setting of inhomogeneity illustrates several nontrivial properties of lattice refinements of discrete quantum gravity. Nevertheless, the situation at the dynamical level is quite nontrivial and thus provides insights to the anomaly problem. At an effective level, consistent versions of the dynamics are presented which implement the conditions together with the dynamical constraints of gravity in an anomaly-free manner. These are then used for analytical as well as numerical investigations of the fate of classical singularities, including nonspacelike ones, as they generically develop in these models. None of the corrections used here resolve those singularities by regular effective geometries. However, there are numerical indications that the collapse ends in a tamer shell-crossing singularity prior to the formation of central singularities for mass functions giving a regular conserved mass density. Moreover, we find quantum gravitational obstructions to the existence of exactly homogeneous solutions within this class of models. This indicates that homogeneous models must be seen in a wider context of inhomogeneous solutions and their reduction in order to provide reliable dynamical conclusions.

In general relativity, one is supposed to derive the metric by solving the relevant Einstein equations. However, the metric for the Friedmann–Lemaitre–Robertson–Walker (FLRW) metric has so far been obtained by starting from Weyl’s postulate and eventually by geometric considerations alone. But here, instead, we rigorously derive the same by solving the Einstein equations appropriate for gravitational collapse/expansion of a perfect fluid. The fact that FLRW metric can indeed be obtained by solving a Einstein equations shows the physical correctness of the Weyl postulate. This exercise thus complements rather than rivals the traditional derivation of the FLRW metric. During this exercise, we derive rather than merely obtain the Hubble’s law. This exercise also confirms that the total energy of the FLRW universe, including matter and gravitation, is indeed given by the well known “Misner-Sharp mass”. With this firm identification, we confirm the intuitive idea that while the “closed model” is gravitationally bound, the “open model” is gravitationally unbound.

Zircon and monazite U–Pb data document the geochronology of the felsic crust in the Mozambique Belt in NE Mozambique. Immediately E of Lake Niassa and NW of the Karoo-aged Maniamba Graben, the Ponta Messuli Complex preserves Paleoproterozoic gneisses with granulite-facies metamorphism dated at 1950 ± 15 Ma, and intruded by granite at 1056 ± 11 Ma. This complex has only weak evidence for a Pan-African metamorphism. Between the Maniamba Graben and the WSW–ENE-trending Lurio (shear) Belt, the Unango and Marrupa Complexes consist mainly of felsic orthogneisses dated between 1062 ± 13 and 946 ± 11 Ma, and interlayered with minor paragneisses. In these complexes, an amphibolite- to granulite-facies metamorphism is dated at 953 ± 8 Ma and a nepheline syenite pluton is dated at 799 ± 8 Ma. Pan-African deformation and high-grade metamorphism are more intense and penetrative southwards, towards the Lurio Belt. Amphibolite-facies metamorphism is dated at 555 ± 11 Ma in the Marrupa Complex and amphibolite- to granulite-facies metamorphism between 569 ± 9 and 527 ± 8 Ma in the Unango Complex. Post-collisional felsic plutonism, dated between 549 ± 13 and 486 ± 27 Ma, is uncommon in the Marrupa Complex but common in the Unango Complex. To the south of the Lurio Belt, the Nampula Complex consists of felsic orthogneisses which gave ages ranging from 1123 ± 9 to 1042 ± 9 Ma, interlayered with paragneisses. The Nampula Complex underwent amphibolite-facies metamorphism in the period between 543 ± 23 to 493 ± 8 Ma, and was intruded by voluminous post-collisional granitoid plutons between 511 ± 12 and 508 ± 3 Ma. In a larger context, the Ponta Messuli Complex is regarded as part of the Palaeoproterozoic, Usagaran, Congo-Tanzania Craton foreland of the Pan-African orogen. The Unango, Marrupa and Nampula Complexes were probably formed in an active margin setting during the Mesoproterozoic. The Unango and Marrupa Complexes were assembled on the margin of the Congo-Tanzania Craton during the Irumidian orogeny (ca. 1020–950 Ma), together with terranes in the Southern Irumide Belt. The distinctly older Nampula Complex was more probably linked to the Maud Belt of Antarctica, and peripheral to the Kalahari Craton during the Neoproterozoic. During the Pan-African orogeny, the Marrupa Complex was overlain by NW-directed nappes of the Cabo Delgado Nappe Complex before peak metamorphism at ca. 555 Ma. The nappes include evidence for early Pan-African orogenic events older than 610 Ma, typical for the Eastern Granulites in Tanzania. Crustal thickening at 555 ± 11 Ma is coeval with high-pressure granulite-facies metamorphism along the Lurio Belt at 557 ± 16 Ma. Crustal thickening in NE Mozambique is part of the main Pan-African, Kuunga, orogeny peaking between 570 and 530 Ma, during which the Congo-Tanzania, Kalahari, East Antarctica and India Cratons welded to form Gondwana. Voluminous post-collisional magmatism and metamorphism younger than 530 Ma in the Lurio Belt and the Nampula Complex are taken as evidence of gravitational collapse of the extensive orogenic domain south of the Lurio Belt after ca. 530 Ma. The Lurio Belt may represent a Pan-African suture zone between the Kalahari and Congo-Tanzania Craton.

Zircon and monazite U-Pb data document the geochronology of the felsic crust in the Mozambique Belt in NE Mozambique. Immediately E of Lake Niassa and NW of the Karoo-aged Maniamba Graben, the Ponta Messuli Complex preserves Paleoproterozoic gneisses with granulite-facies metamorphism dated at 1950 ± 15 Ma, and intruded by granite at 1056 ± 11 Ma. This complex has only weak evidence for a Pan-African metamorphism. Between the Maniamba Graben and the WSW-ENE-trending Lurio (shear) Belt, the Unango and Marrupa Complexes consist mainly of felsic orthogneisses dated between 1062 ± 13 and 946 ± 11 Ma, and interlayered with minor paragneisses. In these complexes, an amphibolite-to granulitefacies metamorphism is dated at 953 ± 8 Ma and a nepheline syenite pluton is dated at 799 ± 8 Ma. Pan-African deformation and high-grade metamorphism are more intense and penetrative southwards, towards the Lurio Belt. Amphibolite-facies metamorphism is dated at 555 ± 11 Ma in the Marrupa Complex and amphibolite-to granulite-facies metamorphism between 569 ± 9 and 527 ± 8 Ma in the Unango Complex. Post-collisional felsic plutonism, dated between 549 ± 13 and 486 ± 27 Ma, is uncommon in the Marrupa Complex but common in the Unango Complex. To the south of the Lurio Belt, the Nampula Complex consists of felsic orthogneisses which gave ages ranging from 1123 ± 9 to 1042 ± 9 Ma, interlayered with paragneisses. The Nampula Complex underwent amphibolite-facies metamorphism in the period between 543 ± 23 to 493 ± 8 Ma, and was intruded by voluminous post-collisional granitoid plutons between 511 ± 12 and 508 ± 3 Ma. In a larger context, the Ponta Messuli Complex is regarded as part of the Palaeoproterozoic, Usagaran, Congo-Tanzania Craton foreland of the Pan-African orogen. The Unango, Marrupa and Nampula Complexes were probably formed in an active margin setting during the Mesoproterozoic. The Unango and Marrupa Complexes were assembled on the margin of the Congo-Tanzania Craton during the Irumidian orogeny (ca. 1020-950 Ma), together with terranes in the Southern Irumide Belt. The distinctly older Nampula Complex was more probably linked to the Maud Belt of Antarctica, and peripheral to the Kalahari Craton during the Neoproterozoic. During the Pan-African orogeny, the Marrupa Complex was overlain by NW-directed nappes of the Cabo Delgado Nappe Complex before peak metamorphism at ca. 555 Ma. The nappes include evidence for early Pan-African orogenic events older than 610 Ma, typical for the Eastern Granulites in Tanzania. Crustal thickening at 555 ± 11 Ma is coeval with high-pressure granulite-facies metamorphism along the Lurio Belt at 557 ± 16 Ma. Crustal thickening in NE Mozambique is part of the main Pan-African, Kuunga, orogeny peaking between 570 and 530 Ma, during which the Congo-Tanzania, Kalahari, East Antarctica and India Cratons welded to form Gondwana. Voluminous post-collisional magmatism and metamorphism younger than 530 Ma in the Lurio Belt and the Nampula Complex are taken as evidence of gravitational collapse of the extensive orogenic domain south of the Lurio Belt after ca. 530 Ma. The Lurio Belt may represent a Pan-African suture zone between the Kalahari and Congo-Tanzania Craton.

Due to the interaction of physics and astrophysics we are witnessing in these years a splendid synthesis of theoretical, experimental and observational results originating from three fundamental physical processes. They were originally proposed by Dirac, by Breit and Wheeler and by Sauter, Heisenberg, Euler and Schwinger. For almost seventy years they have all three been followed by a continued effort of experimental verification on Earth-based experiments. The Dirac process, e + e − → 2γ, has been by far the most successful. It has obtained extremely accurate experimental verification and has led as well to an enormous number of new physics in possibly one of the most fruitful experimental avenues by introduction of storage rings in Frascati and followed by the largest accelerators worldwide: DESY, SLAC etc. The Breit-Wheeler process, 2γ → e + e − , although conceptually simple, being the inverse process of the Dirac one, has been by far one of the most difficult to be verified experimentally. Only recently, through the technology based on free electron X-ray laser and its numerous applications in Earth-based experiments, some first indications of its possible verification have been reached. The vacuum polarization process in strong electromagnetic field, pioneered by Sauter, Heisenberg, Euler and Schwinger, introduced the concept of critical electric field E c = m 2 e c 3 /(e ). It has been searched without success for more than forty years by heavy-ion collisions in many of the leading particle accelerators worldwide.

Convergent plate boundaries are characterized by the development of crustal orogenic wedges and orogenic plateaus but also by gravitational collapse of previously thickened crust leading to the opening of intermontane and eventually oceanic back-arc basins. Foreland and extensional sedimentary basins in the plate boundary region are filled by the erosional products of the orogenic crust. Metamorphic rocks forming orogenic crust attest to burial and exhumation under contrasted geothermal gradients. These features portray the crustal orogenic cycle and are first-order indicators of the thermal and mechanical evolution of the crust within the plate boundary region. This evolution is controlled by complex interactions among (i) the dynamic balance among forces that arise from plate-tectonic, gravitational potential energy, and buoyancy, (ii) the thermal balance between deformation-induced and radioactive heat production and heat advection related to subduction, orogenic deformation, and magma transfer, and (iii) the mass transfer balance between uplift and erosion. To account for these geological characteristics, a generic model, that integrates results from physical modeling, is proposed for the thermal–mechanical evolution of crustal orogenic belts and for its implication in controlling the transition between the different phases of the orogenic cycle. In this model, the transition from low to high geothermal gradient is associated with increased heat production in the thickened crust owing to radioactive decay and deformation. Partial melting and rheologic weakening of the thermally mature thickened crust triggers gravity-driven lateral flow of the lower crust and controls the transition from wedge to orogenic plateau. Destruction of the orogenic crust is achieved in part by erosion but mostly by gravitational collapse. The style of extension is controlled by the rheology of the crust at the onset of gravitational collapse and its evolution as the crust thins and cools. Gravitational collapse is permitted by a modification of lithosphere dynamics in the convergence zone and might eventually lead to opening of a new oceanic basin if collapse is followed by thinning of the lithospheric mantle.

Hoyle & Folwler showed that there could be Radiation Pressure Supported Stars (RPSS) even in Newtonian gravity. Much later, Mitra found that one could also conceive of their General Relativistic (GR) version, "Relativistic Radiation Pressure Supported Stars" (RRPSSs). While RPSSs have z ≪ 1, RRPSSs have z ≫ 1, where z is the surface gravitational redshift. Here we elaborate on the formation of RRPSSs during continued gravitational collapse by recalling that a contracting massive star must start trapping radiation as it would enter its photon sphere. It is found that, irrespective of the details of the contraction process, the trapped radiation flux should attain the corresponding Eddington value at sufficiently large z ≫ 1. This means that continued GR collapse may generate an intermediate RRPSS with z ≫ 1 before a true BH state with z = ∞ is formed asymptotically. An exciting consequence of this is that the stellar mass black hole candidates, at present epoch, should be hot balls of quark gluon plasma, as has been discussed by Royzen in a recent article entitled "QCD against black holes?".

We construct and analyze a large class of exact five-and six-dimensional regular and static solutions of the vacuum Einstein equations. These solutions describe sequences of Kaluza-Klein bubbles and black holes, placed alternately so that the black holes are held apart by the bubbles. Asymptotically the solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they are part of the (µ, n) phase diagram introduced in hep-th/0309116. In particular, they occupy a hitherto unexplored region of the phase diagram, since their relative tension exceeds that of the uniform black string. The solutions contain bubbles and black holes of various topologies, including six-dimensional black holes with ring topology S 3 × S 1 and tuboid topology S 2 × S 1 × S 1 . The bubbles support the S 1 's of the horizons against gravitational collapse. We find two maps between solutions, one that relates fiveand six-dimensional solutions, and another that relates solutions in the same dimension by interchanging bubbles and black holes. To illustrate the richness of the phase structure and the non-uniqueness in the (µ, n) phase diagram, we consider in detail particular examples of the general class of solutions.

The end of major orogenic episodes is marked by uplift and erosion, transcurrent to extensional tectonic regimes induced partly by gravitational collapse of the thickened crust, partly by delamination of the lithosphere, and emplacement of voluminous igneous formations. This period starts soon after the completion of the continent-continent collisional event. Contrasting igneous suites, regarding their nature, evolution and original sources, are emplaced. Two distinctive and successive igneous associations can be evidenced: 0024-4937/$ -see front matter D During postorogenic and within-plate episodes, commingling of mafic and felsic magmas is documented by synplutonic dykes and sills, and by mafic enclaves. Radiogenic isotope systematics suggest that coexisting mafic and felsic magmas come from the same mantle source yielding depleted but LILE-enriched compositions, with subsequent wall-rock crustal contamination. The onset of the magmatic episode is promoted by lithosphere delamination. The role played by continental crust, though still disputed, becomes increasingly minor with time to null.

A comparison of large orogenic belts formed at convergent plate boundaries indicates that orogenic evolution comprises a period of crustal thickening followed by the formation of a continental plateau and commonly syn-to post-convergence extension and thinning of the previously thickened crust. The instantaneous and finite strain patterns recorded in orogenic belts do not appear to be linked in a simple way to plate kinematics. These patterns suggest that deformation of continental crust is not solely controlled by horizontal compression due to plate convergence and that gravity-driven flow is likely to play a significant role on the deformation of thickened crust. Geophysical data in southern Tibet, an actively convergent orogen, and geologic data of the exhumed mid-crustal core of eroded orogens reveals that orogenic crust is affected by widespread partial melting. Partial melting of thermally mature zones of thickened crust results in the generation of a layer of low-viscosity rocks that may affect the behaviour of the orogenic belt. In particular, the presence of this layer favours mechanical decoupling between the subducting plate and the overlying thickened orogenic crust, resulting in flow of the crust driven by contrasts in gravitational potential energy. D 2001 Published by Elsevier Science B.V.

We show by example how the uncoding of Gamma-Ray Bursts (GRBs) offers unprecedented possibilities to foster new knowledge in fundamental physics and in astrophysics. After recalling some of the classic work on vacuum polarization in uniform electric fields by Klein, Sauter, Heisenberg, Euler and Schwinger, we summarize some of the efforts to observe these effects in heavy ions and high energy ion collisions. We then turn to the theory of vacuum polarization around a Kerr-Newman black hole, leading to the extraction of the blackholic energy, to the concept of dyadosphere and dyadotorus, and to the creation of an electron-positron-photon plasma. We then present a new theoretical approach encompassing the physics of neutron stars and heavy nuclei. It is shown that configurations of nuclear matter in bulk with global charge neutrality can exist on macroscopic scales and with electric fields close to the critical value near their surfaces. These configurations may represent an initial condition for the process of gravitational collapse, leading to the creation of an electron-positron-photon plasma: the basic selfaccelerating system explaining both the energetics and the high energy Lorentz factor observed in GRBs. We then turn to recall the two basic interpretational paradigms of our GRB model: 1) the Relative Space-Time Transformation (RSTT) paradigm and 2) the Interpretation of the Burst Structure (IBS) paradigm. These paradigms lead to a "canonical" GRB light curve formed from two different components: a Proper-GRB (P-GRB) and an extended afterglow comprising a raising part, a peak, and a decaying tail. When the P-GRB is energetically predominant we have a "genuine" short GRB, while when the afterglow is energetically predominant we have a so-called long GRB or a "fake" short GRB. We compare and contrast the description of the relativistic expansion of the electron-positron plasma within our approach and within the other ones in the current literature. We then turn to the special role of the baryon loading in discriminating between "genuine" short and long or "fake" short GRBs and to the special role of GRB 991216 to illustrate for the first time the "canonical" GRB bolometric light curve. We then propose a spectral analysis of GRBs, and proceed to some applications: GRB 031203, the first spectral analysis, GRB 050315, the first complete light curve fitting, GRB 060218, the first evidence for a critical value of the baryon loading, GRB 970228, the appearance of "fake" short GRBs. We finally turn to the GRB-Supernova Time Sequence (GSTS) paradigm: the concept of induced gravitational collapse. We illustrate this paradigm by the systems GRB 980425 / SN 1998bw, GRB 030329 / SN 2003dh, GRB 031203 / SN 2003lw, GRB 060218 / SN 2006aj, and we present the enigma of the URCA sources. We then present some general conclusions.

There are many observational evidences for the detection of compact objects with masses significantly larger (in galactic cases) or much larger (in extragalactic cases) than the upper limits of masses of cold Neutron Stars. Such compact objects are commonly interpreted as Black Holes (BHs). However, we point out that while such Black Hole Candidates (BHCs) must be similar to BHs in many respects they, actually, can not be BHs because existence of Black Holes would violate the basic tenet of the General Theory of Relativity that the worldline of a material particle must be timelike at any regular region of spacetime. We arrive at this unique conclusion by approaching the problem from various directions. We feel that such "operational" Black Holes could be able to explain hard X-ray tail found in the galactic BHCs because Lorentz factor of the plasma accreting on such objects should be considerably higher than the corresponding NS case. 1

We review the current theoretical understanding how growth from micro-meter sized dust to massive giant planets occurs in disks around young stars. After introducing a number of observational constraints from the solar system, from observed protoplanetary disks, and from the extrasolar planets, we simplify the problem by dividing it into a number of discrete stages which are assumed to occur in a sequential way. In the first stage - the growth from dust to kilometer sized planetesimals - the aerodynamics of the bodies are of central importance. We discuss both a purely coagulative growth mode, as well as a gravoturbulent mode involving a gravitational instability of the dust. In the next stage, planetesimals grow to protoplanets of roughly 1000 km in size. Gravity is now the dominant force. The mass accretion can be strongly non-linear, leading to the detachment of a few big bodies from the remaining planetesimals. In the outer planetary system (outside a few AU), some of these bodi...

We construct composite CFT operators from a large number of fermionic primary fields corresponding to states that are holographically dual to a zero temperature Fermi gas in AdS space. We identify a large N regime in which the fermions behave as free particles. In the hydrodynamic limit the Fermi gas forms a degenerate star with a radius determined by the Fermi level, and a mass and angular momentum that exactly matches the boundary calculations. Next we consider an interacting regime, and calculate the effect of the gravitational back-reaction on the radius and the mass of the star using the Tolman-Oppenheimer-Volkoff equations. Ignoring other interactions, we determine the "Chandrasekhar limit" beyond which the degenerate star (presumably) undergoes gravitational collapse towards a black hole. This is interpreted on the boundary as a high density phase transition from a cold baryonic phase to a hot deconfined phase.

Following our recent finding [1] that for the final state of continued spherical gravitational collapse of sufficiently massive bodies, the final gravitational mass of the fluid, M f → 0, we show that for a physical fluid the eventual value of 2M f /R f → 1 rather than 2M f /R f < 1 (the speed of light c = 1 and the gravitational constant G = 1), indicating the approach to a zero-mass black hole. We also point out that as the final state is approached the curvature components tend to blow up, also the proper radial distance l and the proper time (measured along a radial worldline) τ → ∞ indicating that actually the singularity is never attained. We also identify that, the final state may correspond to the local 3-speed attaining either V = 0 or V → c, even though invariant circumference contraction speed U = dR/dτ → 0. Nonetheless, at a finite observation epoch, such Eternally Collapsing Objects (ECOs) may have a local speed of collapse V ≪ c and the labframe speed of collapse may be negligible because of high surface gravitational redshift. However, if quantum back reaction in the strong gravity regime would cause a phase transition of the form, pressure p = −ρ, where ρ is the density of the collapsing fluid, it may be possible to have static Ultra Compact Objects (UCOs) of arbitrary high mass [2]. While supposed Black Holes have no intrinsic magnetic field, ECOs or UCOs are likely to possess strong intrinsic magnetic field and we point out that there are already some tentative evidence for existence of such intrinsic magnetic fields in some Black Hole Candidates [3,4]. For the benefit of the readers who may not have gone through Paper I, we also include here the summary of the same. It clearly shows that the central result of Paper I can be derived even without knowing the meaning of the nomenclature V or without imposing any of property of V such as whether V < 1 or not. In addition we consolidate the same result from other physical considerations too. 1

Archean granite–greenstone terranes represent juvenile continental crust formed in a variety of plate tectonic settings and metamorphosed through a complex series of structural and magmatic events. Most Archean granite greenstone terranes appear to have acquired their first-order structural and metamorphic characteristics at convergent plate margins, where large accretionary wedges similar in aspect to the Chugach, Makran, and Altaids grew through offscraping and accretion of oceanic plateaux, oceanic crustal fragments, juvenile island arcs, rifted continental margins, and pelagic and terrigenous sediments. Buoyant slabs of parts of Archean oceanic lithosphere may have been underplated beneath these orogens, forming thick crustal roots characterized by interleaving between the depleted slabs and undepleted asthenosphere. Back-stepping of the subduction zones after accretion of plateaux and arcs caused the arcs magmatic fronts to migrate trenchward through the accretionary wedges. Dehydration of the subducting slabs hydrated the mantle wedges below the new arcs and generated magmas (sanukitoid suite) in the mantle wedge, whereas other magmas (tonalite, trondhjemite, granodiorite or TTG suite) appear to have been generated by melting of hot young subducted slabs. Eventual collision of these juvenile orogens with other continental blocks formed anatectic granites, then thickened the crust beyond its ability to support its own mass, which initiated gravitational collapse and decompressional release of syn- to late-tectonic granitoids from wedges of fertile mantle trapped between underplated oceanic lithospheric slabs, and aided in the cratonization of the granite–greenstone terranes. Deeply penetrating structural discontinuities such as shear zones and sutures provided pathways for fluids and granitoids to migrate into the mid- and upper-crust, forming ore deposits and plutons. Most preserved granite–greenstone terranes have been tectonically stable since the Archean, and form the cratonic interiors of many continents.

The main forces driving black holes, neutron stars, pulsars, quasars, and supernovae dynamics have certain commonality to the mechanisms of less tumultuous systems such as galaxies, stellar and planetary dynamics. They involve gravity, electromagnetic, and single and collective particle processes. We examine the collective coherent structures of plasma and their interactions with the vacuum. In this paper we present a

PREFACE Gravitation (the attractive force existing between any two objects present in the universe that have mass) refers to one of the four fundamental forces in physics that are responsible for the attraction between masses. The other three fundamental forces are strong nuclear power, weak nuclear power and electromagnetism. In comparison to these other three forces, gravitation is certainly the "odd" one. While there is one single theory called the "Grand Unified Theory" that describes the other three forces, gravitation is explained solely by Einstein's general theory of relativity. According to that general theory of relativity, masses cause a distortion of the space-time structure around them. Any other mass that comes closer will experience the warping of space-time, and this appears to us as an attractive force between two masses. We will reason that this view is the wrong side of the coin. By turning over that same coin, another possibility appears that has a much stronger argument and brings out the true nature of gravitation. In that search, a number of fixed assumptions were reviewed and there, too, surprising new insights emerged. The phenomenon of the "spin" of elementary particles finally gets a plausible explanation, the reason for the expansion of the universe and the consequences involved showing a different reality, and the key in the lock of the Grand Unification theory has been turned, opening up a new dimension in physics. Let us take a first step : " … Einstein himself believed that the theory of general relativity could not properly function without a medium … " so the big question is where to look for that nebulous concept and determine what its energetic signature is?

The Araçuaí Fold Belt was defined as the southeastern limit of the São Francisco Craton in the classical paper published by Fernando Flávio Marques de Almeida in 1977. This keystone of the Brazilian geologic literature catalyzed important discoveries, such as of Neoproterozoic ophiolites and a calc-alkaline magmatic arc, related to the Araçuaí Belt and paleotectonic correlations with its counterpart located in Africa (the West Congo Belt), that provided solid basis to define the Araçuaí-West-Congo Orogen by the end of the 1990 th decade. After the opening of the Atlantic Ocean in Cretaceous times, two thirds of the Araçuaí-West-Congo Orogen remained in the Brazil side, including records of the continental rift and passive margin phases of the precursor basin, all ophiolite slivers and the whole orogenic magmatism formed from the pre-collisional to post-collisional stages. Thus, the name Araçuaí Orogen has been applied to the Neoproterozoic-Cambrian orogenic region that extends from the southeastern edge of the São Francisco Craton to the Atlantic coastline and is roughly limited between the 15º and 21º S parallels. After 30 years of systematic geological mapping together with geochemical and geochronological studies published by many authors, all evolutionary stages of the Araçuaí Orogen can be reasonably interpreted. Despite the regional metamorfism and deformation, the following descriptions generally refer to protoliths. All mentioned ages were obtained by U-Pb method on zircon. The Macaúbas Group records rift, passive margin and oceanic environments of the precursor basin of the Araçuaí Orogen. From the base to the top and from proximal to distal units, this group comprises the pre-glacial Duas Barras and Rio Peixe Bravo formations, and the glaciogenic Serra do Catuni, Nova Aurora and Lower Chapada Acauã formations, related to continental rift and transitional stages, and the diamictitefree Upper Chapada Acauã and Ribeirão da Folha formations, representing passive margin and oceanic environments. Dates of detrital zircon grains from Duas Barras sandstones and Serra do Catuni diamictites suggest a maximum sedimentation age around 900 Ma for the lower Macaúbas Group, in agreement with ages yielded by the Pedro Lessa mafic dikes (906 ± 2 Ma) and anorogenic granites of Salto da Divisa (875 ± 9 Ma). The thick diamictite-bearing marine successions with sand-rich turbidites, diamictitic iron formation, mafic volcanic rocks and pelites (Nova Aurora and Lower Chapada Acauã formations) were deposited from the rift to transitional stages. The Upper Chapada Acauã Formation consists of a sand-pelite shelf succession, deposited after ca. 864 Ma ago in the proximal passive margin. The Ribeirão da Folha Formation mainly consists of sand-pelite turbidites, pelagic pelites, sulfide-bearing cherts and banded iron formations, representing distal passive margin to oceanic sedimentation. Gabbro and dolerite with plagiogranite veins dated at ca. 660 Ma, and ultramafic rocks form tectonic slices of oceanic lithosphere thrust onto packages of the Ribeirão da Folha Formation. The pre-collisional, calc-alkaline, continental magmatic arc (G1 Suite, 630-585 Ma) consists of tonalites and granodiorites, with minor diorite and gabbro. A volcano-sedimentary succession of this magmatic arc includes pyroclastic and volcaniclastic rocks of dacitic composition dated at ca. 585 Ma, ascribed to the Palmital do Sul and Tumiritinga formations (Rio Doce Group), deposited from intra-arc to fore-arc settings. Detrital zircon geochronology suggests that the São Tomé wackes (Rio Doce Group) represent intra-arc to back-arc sedimentation after ca. 594 Ma ago. The Salinas Formation, a conglomerate-wacke-pelite association located to northwest of the magmatic arc, represents synorogenic sedimentation younger than ca. 588 Ma. A huge zone of syn-collisional S-type granites (G2 Suite, 582-560 Ma) occurs to the east and north of the pre-collisional magmatic arc, northward of latitude 20º S. Partial melting of G2 granites originated peraluminous leucogranites (G3 Suite) from the late-to post-collisional stages. A set of late structures, and the post-collisional intrusions of the S-type G4 Suite (535-500 Ma) and I-type G5 Suite (520-490 Ma) are related to the gravitational collapse of the orogen. The location of the magmatic arc, roughly parallel to the zone with ophiolite slivers, from the 17º30' S latitude southwards suggests that oceanic crust only developed along the southern segment of the precursor basin of the Araçuaí-West-Congo Orogen. This basin was carved, like a large gulf partially floored by oceanic crust, into the São Francisco-Congo Paleocontinent, but paleogeographic reconstructions show that the Bahia-Gabon cratonic bridge (located to the north of the Araçuaí Orogen) subsisted since at least 1 Ga until the Atlantic opening. This uncommon geotectonic scenario inspired the concept of confined orogen, quoted as a new type of collisional orogen in the international literature, and the appealing nutcracker tectonic model to explain the Araçuaí-West-Congo Orogen evolution.

... assess sediment failure relates to the impossibility of correlating, from headwall to toe regions of ... and Tucker, 1997] , [Payros et al., 1999] , [Cronin et al., 2000] , [Graziano, 2001] , [Lucente ... of stratified Prina series NE of the village of Kalamavka (location 12); (f) isolated carbonate ...

We invoke the global properties of the actual GTR field equations for spherical collapse to directly show that the condition for formation of trapped surfaces, 2GM/R &gt;1 is not allowed by GTR. And therefore all singularity theorems based on the assumption of formation of trapped surfaces are invalidated! Our conclusion is in perfect agreement with Einstein&#39;s intuitive idea that a Sch. like surface can not occur in reality. Further as singularity is approached R -&gt;0, in order that 2GM/R 0! Harrison, et al. had also pointed out that collapse should come to a decisive end with M=0. This is possible in GTR if the fluid radiates its entire original mass-energy during the relentless graviatational contraction process, Q-&gt;M c^2! Since the actual efficiency for gamma ray production by the relevant blast wave may hardly exceed 10-20% and there could be a stronger (undetected) nu-anti-nu burst precding GRBs, the actual energy released for GRB 990123, even accounting for probable w...

We describe here the LVD experiment (Large-Volume Detector) of the Gran Sasso Laboratory, which is the natural improvement of the LSD experiment (Liquid Scintillation Detector) running in the Mont Blanc Laboratory. The LVD ((31×13) m2 area, height 12 m) consists of ≈1800 tons of liquid scintillator and of a system of streamer tubes on 5 layers for reconstructing tracks of charged particles. As any experiment in an underground laboratory, which has a low statistics of events and requires long running times, the LVD is a multipurpose experiment but with different priorities of the researches. The main goal is neutrino astronomy, firstly detection of neutrinos from collapsing stars and secondly high-energy neutrinos and solar neutrinos. Since the expected number of interactions of neutrinos, from a stellar collapse is very high (of order of 900 for a collapse at the distance of the galactic centre), the LVD is, contrary to the present experiments, a real neutrino observatory, able to make a detailed analysis of the energy and temporal distributions of the burst. In addition to neutrino astrophysics, with the LVD experiment excellent possibilities exist to perform researches in cosmic-ray and high-energy elementary-particle physics. Si descrive l'esperimento LVD (Large Volume Detector) del laboratorio del Gran Sasso, che rappresenta il naturale sviluppo dell'esperimento LSD (Liquid Scintillation Detector) in funzione nel laboratorio del Monte Bianco. LVD (area (31×13) m2, altezza 12 m) consiste di ∼1800 tonnellate di scintillatore liquido e di un sistema di tubi a streamer su 5 piani per la ricostruzione delle tracce di particelle cariche. Come tutti gli esperimenti in laboratori sotterranei, che sono a tempi lunghi ed a bassa statistica, l'esperimento LVD è a multiscopi ma con diverse priorità delle ricerche. L'obiettivo principale è l'astronomia neutrinica, in primo luogo la rivelazione di neutrini da collassi gravitazionali stellari, e poi neutrini di alta energia e neutrini solari. Dato l'alto numero previsto di interazioni di neutrini (∼900 per un collasso alla distanza del centro galattico) da stelle collassanti, l'esperimento LVD costituisce, a differenza degli attuali esperimenti, un vero e proprio osservatorio neutrinico, in grado di compiere un'analisi dettagliata delle distribuzioni energetica e temporale del burst. Oltre all'astrofisica neutrinica, con l'esperimento LVD si possono compiere ricerche in fisica della radiazione cosmica e di particelle elementari ad altissime energie. В данной работе описывается зксперимент LVD (Large Volume Detector), который будет проводиться в лаборатории Гран Cacco. LVD является естественным продолжением эксперимента LSD (Liquid Scintillation Detector) в лаборатории Монблан. LVD (площадь (31×13) м2, высота 12 м) содержит 1800 тонн жидкого сцинтиллятора и включает в себя систему стримерных детекторов, размещенных на 5 уровнях. Последние используются для реконструкции треков заряженных частиц. Как и любой длительный эксперимент в подземных условиях, когда статистика событий невелика, LVD имеет многоцелевое назначение. Научные программы, однако, будут обладать различным приоритетом. Основное внимание будет уделяться нейтринной астрономии, и в первую очередь— детектированию нейтрино от коллапсирующих звезд. Кроме того, будут проводиться исследования по регистрации нейтрино высоких энергий и солнечных нейтрино. Поскольку ожидаемое количество взаимодействий в случае прихода потока нейтрино от коллапса очень велико, порядка 900, LVD будет настоящей нейтринной обсерваторией, способной, в отличие от ведущихся сейчас экспериментов, детально исследовать энергетическое временное распределения для вспышки нейтринного излучения. В дополнение к нейтринной астрофизике, имеются очень хорошие перспективы и для исследований в области космических лучей и физики элементарных частиц высоких энергий.

We review the current theoretical understanding how growth from micrometer sized dust to massive giant planets occurs in disks around young stars. After introducing a number of observational constraints from the solar system, from observed protoplanetary disks, and from the extrasolar planets, we simplify the problem by dividing it into a number of discrete stages which are assumed to occur in a sequential way. In the first stage -the growth from dust to kilometer sized planetesimals -the aerodynamics of the bodies are of central importance. We discuss both a purely coagulative growth mode, as well as a gravoturbulent mode involving a gravitational instability of the dust. In the next stage, planetesimals grow to protoplanets of roughly 1000 km in size. Gravity is now the dominant force. The mass accretion can be strongly non-linear, leading to the detachment of a few big bodies from the remaining planetesimals. In the outer planetary system (outside a few AU), some of these bodies can become so massive that they eventually accrete a large gaseous envelope. This is the stage of giant planet formation, as understood within the core accretiongas capture paradigm. We also discuss the direct gravitational collapse model where giant planets are thought to form directly via a gravitational fragmentation of the gas disk. In the inner system, protoplanets collide in the last stage -probably after the dispersal of the gaseous disk -in giant impacts until the separations between the remaining terrestrial planets become large enough to allow long term stability. We finish the review with some selected questions.

Archean granite–greenstone terranes represent juvenile continental crust formed in a variety of plate tectonic settings and metamorphosed through a complex series of structural and magmatic events. Most Archean granite greenstone terranes appear to have acquired their first-order structural and metamorphic characteristics at convergent plate margins, where large accretionary wedges similar in aspect to the Chugach, Makran, and Altaids grew through offscraping and accretion of oceanic plateaux, oceanic crustal fragments, juvenile island arcs, rifted continental margins, and pelagic and terrigenous sediments. Buoyant slabs of parts of Archean oceanic lithosphere may have been underplated beneath these orogens, forming thick crustal roots characterized by interleaving between the depleted slabs and undepleted asthenosphere. Back-stepping of the subduction zones after accretion of plateaux and arcs caused the arcs magmatic fronts to migrate trenchward through the accretionary wedges. Dehydration of the subducting slabs hydrated the mantle wedges below the new arcs and generated magmas (sanukitoid suite) in the mantle wedge, whereas other magmas (tonalite, trondhjemite, granodiorite or TTG suite) appear to have been generated by melting of hot young subducted slabs. Eventual collision of these juvenile orogens with other continental blocks formed anatectic granites, then thickened the crust beyond its ability to support its own mass, which initiated gravitational collapse and decompressional release of syn- to late-tectonic granitoids from wedges of fertile mantle trapped between underplated oceanic lithospheric slabs, and aided in the cratonization of the granite–greenstone terranes. Deeply penetrating structural discontinuities such as shear zones and sutures provided pathways for fluids and granitoids to migrate into the mid- and upper-crust, forming ore deposits and plutons. Most preserved granite–greenstone terranes have been tectonically stable since the Archean, and form the cratonic interiors of many continents.

Gravitational collapse is one of the most fruitful subjects in gravitational physics. It is well known that singularity formation is inevitable in complete gravitational collapse. It was conjectured that such a singularity should be hidden by horizons if it is formed from generic initial data with physically reasonable matter fields. Many possible counterexamples to this conjecture have been proposed over the past three decades, although none of them has proved to be sufficiently generic. In these examples, there appears a singularity that is not hidden by horizons. This singularity is called a 'naked singularity.' The appearance of a naked singularity represents the formation of an observable high-curvature, strong-gravity region. In this paper we review examples of naked singularity formation and recent progress in research of observable physical processes -gravitational radiation and quantum particle creation -from a forming naked singularity. * )

We investigate the evolution of rigidly and differentially rotating protoneutron stars during the first twenty seconds of their life. We solve the equations describing stationary axisymmetric configurations in general relativity coupled to a finite temperature, relativistic equation of state, to obtain a sequence of quasi-equilibrium configurations describing the evolution of newly born neutron stars. The initial rotation profiles have been taken to mimic the situation found immediately following the gravitational collapse of rotating stellar cores. By analyzing the output of several models, we estimate that the scale of variation of the angular velocity in a newly born neutron star is of the order of 7−10 km. We obtain the maximum rotation frequency that can be reached as the protoneutron stars deleptonizes and cools down, as well as other relevant parameters such as total angular momentum or the instability parameter |T/W|. Our study shows that imposing physical constraints (conservation of baryonic mass and angular momentum) and choosing reasonable thermodynamical profiles as the star evolves gives results consistent with the energetics of more complex simulations of non-rotating protoneutron stars. It appears to be unlikely that newly born protoneutron stars formed in nearly axisymmetric core collapses reach the critical angular velocity to undergo the bar mode instability. They could, however, undergo secular or low |T/W| rotational instabilities a few seconds after birth, resulting in a strong emission of gravitational waves retarded with respect to the neutrino luminosity peak. We also found that the geometry of strongly differentially rotating protoneutron stars can become toroidal-like for large values of the angular velocity, before reaching the mass shedding limit.

The Citlaltépetl-Cofre de Perote volcanic chain forms an important physiographic barrier that separates the Central Altiplano (2500 masl) from the Gulf Coastal Plain (GCP) (1300 masl). The abrupt eastward drop in relief between these provinces gives rise to unstable conditions and consequent gravitational collapse of large volcanic edifices built at the edge of the Altiplano. Eastward sloping substrate, caused by the irregular configuration of the basement rocks, is the dominant factor that controls the direction of collapsing sectors in all major volcanoes in the region to be preferentially towards the GCP. These collapses produced voluminous debris avalanches and lahars that inundated the well-developed drainages and clastic aprons that characterize the Coastal Plain. Large catastrophic collapses from Citlaltépetl, Las Cumbres, and Cofre de Perote volcanoes are well documented in the geologic record. Some of the avalanches and transformed flows have exceptionally long runouts and reach the Gulf of Mexico traveling more than 120 km from their source. So far, no direct evidence has been found for magmatic activity associated with the initiation of these catastrophic flank-collapses. Apparently, instability of the volcanic edifices has been strongly favored by very intense hydrothermal alteration, abrupt topographic change, and intense fracturing. In addition to the eastward slope of the substrate, the reactivation of pre-volcanic basement structures during the Late Tertiary, and the E-W to ENE-SSW oriented regional stress regimes may have played an important role in the preferential movement direction of the avalanches and flows. In addition to magmatic-hydrothermal processes, high amounts of rainfall in the area is another factor that enhances alteration and eventually weakens the rocks. It is very likely that seismic activity may be the principal triggering mechanism that caused the flank collapse of large volcanic edifices in the Eastern Mexican Volcanic Belt. However, critical pore water pressure from extraordinary amounts of rainfall associated with hurricanes or other meteorological perturbation cannot be ruled out, particularly for smaller volume collapses. There are examples in the area of small seismogenic debris flows that have occurred in historical times, showing that these processes are not uncommon. Assessing the stability conditions of major volcanic edifices that have experienced catastrophic sector collapses is crucial for forecasting future events. This is particularly true for the Eastern Mexican Volcanic Belt, where in many cases no magmatic activity was associated with the collapse. Therefore, edifice failure could occur again without any precursory warning.

The E-W-opening Tyrrhenian Sea developed after the Cretaceous-Palaeogene Alpine collision, nearly perpendicular to the motion of the African plate, as a back-arc of the Adria-Ionian westward subduction. Three driving mechanisms have been proposed to explain the dynamic evolution of the Tyrrhenian-Apennine system: ( 1 ) the northward indentation of the African plate; (2) the retreating subduction of the Adria-Ionian lithosphere; and (3) the gravitational collapse of the Alpine post-collisional wedge. In order to define the relative contribution of each of these mechanisms in the Neogene dynamic of the Tyrrhenian-Apennine system, we performed 3-D laboratory experiments, in which we simulated a retreating subduction process in a compressional regime oriented perpendicularly to the direction of subduction; in this framework we also tested the influence of the gravitational collapse of the overriding plate. Experiments were constructed using dry sand and silicone putties to simulate brittle upper crust and ductile lower crust/upper mantle, respectively; these layers floated on a highdensity, low-viscosity glucose syrup which simulated the asthenosphere. The main conclusion of our experiments is that large-scale continental extension, similar to that observed in the Tyrrhenian area, could be reproduced perpendicular to the shortening direction induced by the indentation of the African plate; in this framework, extensional processes are indeed possible if the trench retreat velocity is higher than the rate of shortening induced by the advancing African plate. Our experimental results indicate that this high trench retreat velocity could be explained by the coexistence of the gravitational collapse of the post-Alpine wedge with a slab-pull process, linked to the retreating subduction of the Adria-Ionian plate. While the first mechanism is predominant in the Northern Tyrrhenian area, the second one seems to be important in the latest stage of extension and oceanic accretion of the Southern Tyrrhenian area.

RESUMEN En el centro y norte de México los conjuntos litológicos deformados por acortamiento hacia el final del Cretácico e inicios del Cenozoico han sido considerados como producto de la orogenia Laramide. Se hace alusión a esta orogénesis al referirse a las secuencias sedimentarias del centro, oriente y sur del país, ya que la “deformación Laramide” es el evento de acortamiento más joven, y sobrepuesta a esta deformación solo se reconocen estructuras asociadas a tectónica lateral y extensional. El objetivo principal ...

The question of the stability of matter against gravitational collapse is of general interest to astrophysics. In this work we investigate the stability against small radial oscillations of equilibrium configurations of cold, gravitationally bound states of complex scalar fields, known as boson stars. These equilibrium configurations exhibit a mass profile against central density which is very similar to that of ordinary neutron stars, with a pronounced maximum mass at M c = 0.633Mgl/m, where MpI is the Planck mass, for a certain value of the central density %(0). We give analytical and numerical proof that configurations with central densities greater than %(0) are unstable against radial perturbations by studying the behavior of the eigenfrequencies of the perturbations for different values of o(0).

(Some reference links may require a separate subscription.) ... S. Chandrasekhar, Monthly Notices Roy. Astron. Soc. 91, 456 (1931) [ADS]; L. Landau, Phys. Z. USSR 1, 285 (1932). ... Kip S. Thorne, California Institute of Technology Report, 1968 (unpublished).

Most general relativity textbooks devote considerable space to the simplest example of a black hole containing a singularity, the Schwarzschild geometry. However only a few discuss the dynamical process of gravitational collapse, by which black holes and singularities form. We present here two types of analytic models for this process, which we believe are the simplest available; the first involves collapsing spherical shells of light, analyzed mainly in Eddington-Finkelstein coordinates; the second involves collapsing spheres filled with a perfect fluid, analyzed mainly in Painleve-Gullstrand coordinates. Our main goal is pedagogical simplicity and algebraic completeness, but we also present some results that we believe are new, such as the collapse of a light shell in Kruskal-Szekeres coordinates.

Abstract. In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature ~ ~ 10 where ~ is the surface gravity of the black ...

We investigate the global Cauchy problem for a class of semilinear hyperbolic systems where the interaction can be non local in space and time. We establish global existence theorems for the initial value problem when the non linearity is dissipative in a weak sense, and satisfies the causality condition. The argument is abstract and the technique is based on the non-linear resolvent. We apply these results to get low regularity global solutions of several models for relativistic field theory : the Dirac-Maxwell-Klein-Gordon system, and the Thirring model on the Minkowski spacetime R 1+1 ; the Dirac-Klein-Gordon system on Schwarzschild type manifolds, or outside a star undergoing a gravitational collapse to a black-hole. Problème de Cauchy global pour des systèmes hyperboliques semi-linéaires avec interactions non locales. Applicationsà deséquations de Dirac. Résumé. On résoud le problème de Cauchy global pour une classe de systèmes hyperboliques dont l'interaction peutêtre non locale en espace-temps. Nousétablissons des théorèmes d'existence globale quand la non linéarité satisfait une propriété faible de dissipativité, et la condition de causalité. L'argument est abstrait et repose sur une technique de résolvant non linéaire. Nous appliquons ces résultats pour obtenir des solutions globales peu régulières de divers modèles de la théorie relativiste des champs : le système de Dirac-Maxwell-Klein-Gordon et le modèle de Thirring sur l'espace temps de Minkowski R 1+1 ; le système de Dirac-Klein-Gordon dans des variétés de type Schwarzschild, ouà l'extérieur d'uneétoile en effondrement gravitationnel vers un trou noir.

We develop here a new procedure within Einstein's theory of gravity to generate equilibrium configurations that result as the final state of gravitational collapse from regular initial conditions. As a simplification, we assume that the collapsing fluid is supported only by tangential pressure. We show that the equilibrium geometries generated by this method form a subset of static solutions to the Einstein equations, and that they can either be regular or develop a naked singularity at the center. When a singularity is present, there are key differences in the properties of stable circular orbits relative to those around a Schwarzschild black hole with the same mass. Therefore, if an accretion disk is present around such a naked singularity it could be observationally distinguished from a disk around a black hole.