Papers by Zacharias Roupas
AIP Conf. Proc. 2872, 060012 (2023), Sep 11, 2023
Symmetry, Nov 21, 2019
Thermal energy points towards a disordered, completely uniform state act to counter gravity's ten... more Thermal energy points towards a disordered, completely uniform state act to counter gravity's tendency to generate order and structure through gravitational collapse. It is, therefore, expected to contribute to the stabilization of a self-gravitating, classical ideal gas over collapse. However, I identified an instability that always occurs at sufficiently high energies: the high-energy or relativistic gravothermal instability. I argue here that this instability presents an analogous core-halo structure as its Newtonian counterpart, the Antonov instability. The main difference is that in the former case the core is dominated by the gravitation of thermal energy and not rest mass energy. A relativistic generalization of Antonov's instability-the low-energy gravothermal instability-also occurs. The two turning points, which make themselves evident as a double spiral of the caloric curve, approach each other as relativistic effects become more intense and eventually merge in a single point. Thus, the high and low-energy cases may be realized as two aspects of a single phenomenon-the gravothermal instability-which involves a core-halo separation and an intrinsic heat flow. Finally, I argue that the core formed during a core-collapse supernova is subject to the relativistic gravothermal instability if it becomes sufficiently hot and compactified at the time of the bounce. In this case, it will continue to collapse towards the formation of a black hole.
Physics of the Dark Universe
We derive the dark energy fluid equation of state = − = const. as an extremum of entropy, subject... more We derive the dark energy fluid equation of state = − = const. as an extremum of entropy, subject to the Hamiltonian constraint of General Relativity. However, we identify perturbations that can render this extremum an entropy minimum designating a thermodynamic instability and specify the mathematical condition for this to occur.
arXiv (Cornell University), May 21, 2013
Thermodynamical stability of fluid spheres is studied in the presence of a cosmological constant,... more Thermodynamical stability of fluid spheres is studied in the presence of a cosmological constant, both in the Newtonian limit, as well as in General Relativity. In all cases, an increase of the cosmological constant tends to stabilize the system, making asymptotically de Sitter space more thermodynamically stable than anti-de Sitter at the purely classical level. In addition, in the Newtonian case reentrant phase transitions are observed for a positive cosmological constant, due to its repelling property in this case. In General Relativity is studied the case of radiation, for which is found that the critical radius, at which an instability sets in, is always bigger than the black hole radius of the system and furthermore, at some value of the cosmological constant this critical radius hits at the cosmological horizon.
The European Physical Journal C, 2022
While spacetime in the vicinity outside astrophysical black holes is believed to be well understo... more While spacetime in the vicinity outside astrophysical black holes is believed to be well understood, the event horizon and the interior remain elusive. Here, we discover a degenerate infinite spectrum of novel general relativity solutions with the same mass-energy and entropy that describe a dark energy universe inside an astrophysical black hole. This regular cosmological black hole is stabilized by a finite tangential pressure applied on the dual cosmological-black hole event horizon, localized up to a quantum indeterminacy. We recover the Bekenstein–Hawking entropy formula from the classical fluid entropy, calculated at a Tolman temperature equal to the cosmological horizon temperature. We further calculate its gravitational quasi-normal modes. We find that cosmological black holes are detectable by gravitational-wave experiments operating within the$$\mu \mathrm{Hz}$$μHz–$$\mathrm{Hz}$$Hzrange, like LISA space-interferometer.
Communications in Theoretical Physics, 2020
Gravity and thermal energy are universal phenomena which compete over the stabilization of astrop... more Gravity and thermal energy are universal phenomena which compete over the stabilization of astrophysical systems. The former induces an inward pressure driving collapse and the latter a stabilizing outward pressure generated by random motion and energy dispersion. Since a contracting self-gravitating system is heated up one may wonder why is gravitational collapse not halted in all cases at a sufficient high temperature establishing either a gravo-thermal equilibrium or explosion. Here, based on the equivalence between mass and energy, we show that there always exists a temperature threshold beyond which the gravitation of thermal energy overcomes its stabilizing pressure and the system collapses under the weight of its own heat.
Journal of Statistical Mechanics: Theory and Experiment, 2021
The problem of time is a notable obstacle towards the recognition of quantum theory as the ultima... more The problem of time is a notable obstacle towards the recognition of quantum theory as the ultimate fundamental description of nature. Quantum theory may not be complete if founded upon classical notions. Louis de Broglie, seeming to be more or less convinced about the ontology of his proposed matter waves, tried to develop a theory of sub-quantum degrees of freedom relying on statistical thermodynamics. He realized a quantum particle as a fluctuating dense corpuscle formed via non-linear effects from a sub-quantum medium. A wave on the medium guides the vibrating corpuscle. He argued that an intrinsic clock of a quantum particle is related to its Brownian motion at the sub-quantum level. This led him to conjecture a relation between the de Broglie clock frequency mc 2 /h and its implicit temperature, which equals that of the surrounding subquantum medium. About the same time, Mandelbrot was the first to derive in a classical setting a thermodynamic uncertainty relation between energy and temperature, that was, coincidentally or not, anticipated by Bohr and Heisenberg in the first years of development of quantum theory. We show here that, when the de Broglie temperature-time conjecture is assumed, the thermodynamic temperature-energy uncertainty relation leads to the quantum time-energy uncertainty relation.
Astrophysics and Space Science, 2021
The gravitational-wave signal GW190814 involves a compact object with mass (2.50 − 2.67)M⊙ within... more The gravitational-wave signal GW190814 involves a compact object with mass (2.50 − 2.67)M⊙ within the so-called low mass gap. As yet, a general consensus on its nature, being a black hole, a neutron star or an exotic star, has not been achieved. We investigate the possibility this compact object to be an anisotropic neutron star. Anisotropies in a neutron star core arise naturally by effects such as superfluidity, hyperons, strong magnetic fields and allow the maximum mass to exceed that of the ideally isotropic stars. We consider the Krori-Barua ansatz to model an anisotropic core and constrain the equation of state with LIGO/Virgo observations GW170817 and GW190814. We find that the GW190814 secondary component can be an anisotropic neutron star compatible with LIGO/Virgo constraints if the radius attains a value in the range (13.2 − 14.0) km with the anisotropic core's boundary density in the range (3.5 − 4.0) • 10 14 g/cm 3 .
Classical and Quantum Gravity, 2020
It is shown here in the framework of standard General Relativity that the gravitational potential... more It is shown here in the framework of standard General Relativity that the gravitational potential in static spacetime, equivalently the redshift factor, inside any kind of matter, can be derived from maximum entropy principle. It is used only the Hamiltonian constraint, without further invoking Einstein's equations or any new principle. The Newtonian potential arises from the same procedure.
The European Physical Journal C, 2020
Dense nuclear matter is expected to be anisotropic due to effects such as solidification, superfl... more Dense nuclear matter is expected to be anisotropic due to effects such as solidification, superfluidity, strong magnetic fields, hyperons, pion-condensation. Therefore an anisotropic neutron star core seems more realistic than an ideally isotropic one. We model anisotropic neutron stars working in the Krori–Barua (KB) ansatz without preassuming an equation of state. We show that the physics of general KB solutions is encapsulated in the compactness. Imposing physical and stability requirements yields a maximum allowed compactness $$2GM/Rc^2 < 0.71$$ 2 G M / R c 2 < 0.71 for a KB-spacetime. We further input observational data from numerous pulsars and calculate the boundary density. We focus especially on data from the LIGO/Virgo collaboration as well as recent independent measurements of mass and radius of miilisecond pulsars with white dwarf companions by the Neutron Star Interior Composition Explorer (NICER). For these data the KB-spacetime gives the same boundary density wh...
Physical Review D, 2021
At sufficiently high densities and low temperatures matter is expected to behave as a degenerate ... more At sufficiently high densities and low temperatures matter is expected to behave as a degenerate Fermi gas of quarks forming Cooper pairs, namely a color superconductor, as was originally suggested by Alford, Rajagopal and Wilczek. The ground state is a superfluid, an electromagnetic insulator that breaks chiral symmetry, called the color-flavor locked phase. If such a phase occurs in the cores of compact stars, the maximum mass may exceed that of hadronic matter. The gravitationalwave signal GW190814 involves a compact object with mass 2.6M⊙, within the so-called low mass gap. Since it is too heavy to be a neutron star and too light to be a black hole, its nature has not been identified with certainty yet. Here, we show not only that a color-flavor locked quark star with this mass is viable, but also we calculate the range of the model-parameters, namely the color superconducting gap ∆ and the bag constant B, that satisfies the strict LIGO constraints on the equation of state. We find that a color-flavor locked quark star with mass 2.6M⊙ satisfies the observational constraints on the equation of state if ∆ ≥ 200MeV and B ≥ 83MeV/fm 3 for a strange quark mass ms = 95 MeV/c 2 , and attains a radius (12.7 − 13.6)km and central density (7.5 − 9.8)10 14 g/cm 3 .
Astronomy & Astrophysics, 2021
Recent theoretical and numerical developments supported by observational evidence strongly sugges... more Recent theoretical and numerical developments supported by observational evidence strongly suggest that many globular clusters host a black hole (BH) population in their centers. This stands in contrast to the prior long-standing belief that a BH subcluster would evaporate after undergoing core collapse and decoupling from the cluster. In this work, we propose that the inhomogeneous Brownian motion generated by fluctuations of the tellar gravitational field may act as a mechanism adding a stabilizing pressure to a BH population. We argue that the diffusion equation for Brownian motion in an inhomogeneous medium with spatially varying diffusion coefficient and temperature, which was first discovered by Van Kampen, also applies to self-gravitating systems. pplying the stationary phase space probability distribution to a single BH immersed in a Plummer globular cluster, we infer that it may wander as far as ∼0.05, 0.1, 0.5 pc for a mass ofmb ∼ 103, 102, 10 M⊙, respectively. urtherm...
Monthly Notices of the Royal Astronomical Society, 2020
Fuzzy dark matter (FDM) consisting of ultralight axions has been invoked to alleviate galactic-sc... more Fuzzy dark matter (FDM) consisting of ultralight axions has been invoked to alleviate galactic-scale problems in the cold dark matter scenario. FDM fluctuations, created via the superposition of waves, can impact the motion of a central supermassive black hole (SMBH) immersed in an FDM halo. The SMBH will undergo a random walk, induced by FDM fluctuations, that can result in its ejection from the central region. This effect is strongest in dwarf galaxies, accounting for wandering SMBHs and the low detection rate of active galactic nuclei in dwarf spheroidal galaxies. In addition, a lower bound on the allowed axion masses is inferred both for Sagitarius A* and heavier SMBH; to avoid ejection from the galactic centres, axion masses of the order of 10−22 eV or lighter are excluded. Stronger limits are inferred for merging galaxies. We find that the event rate of SMBH mergers in FDM haloes and the associated SMBH growth rates can be reduced by at least an order of magnitude.
Journal of Physics A: Mathematical and Theoretical, 2019
I consider a self-gravitating, N-body system assuming that the N constituents follow regular orbi... more I consider a self-gravitating, N-body system assuming that the N constituents follow regular orbits about the center of mass of the cluster, where a central massive object may be present. I calculate the average over a characteristic timescale of the full, N-body Hamiltonian including all kinetic and potential energy terms. The resulting effective system allows for the identification of the orbital planes with N rigid, disk-shaped tops, that can rotate about their fixed common centre and are subject to mutual gravitational torques. The time-averaging imposes boundaries on the canonical generalized momenta of the resulting canonical phase space. I investigate the statistical mechanics induced by the effective Hamiltonian on this bounded phase space and calculate the thermal equilibrium states. These are a result of the relaxation of spins' directions, identified with orbital planes' orientations, which is called vector resonant relaxation. I calculate the dependence of spins' angular velocity dispersion on temperature and calculate the velocity distribution functions. I argue that the range of validity of the gravitational phase transitions, identified in the special case of zero kinetic term by Roupas, Kocsis & Tremaine, is expanded to non-zero values of the ratio of masses between the cluster of N-bodies and the central massive object. The relevance with astrophysics is discussed focusing on stellar clusters. The same analysis performed on an unbounded phase space accounts for continuous rigid tops. timescales. The orbital angular momentum's vectors' directions (the orbital planes' orientations) relax in several, realistic circumstances independently from their magnitudes, in which case the process is called Vector Resonant Relaxation (VRR). The relaxation of orbital angular momentum's magnitudes is called Scalar Resonant Relaxation. Resonant Relaxation has been studied in astrophysical settings [32-36] especially with numerical simulations [37-40], but also on a kinetic theory basis [41-45]. The method of time-averaging of gravitational orbits and their approximation with rigid wires was introduced by Gauss and has been extensively used in planetary dynamics [46]. In Ref. [47], the time-averaging was applied in a VRR system without any reference to a kinetic energy term. A dynamics of non-canonical variables (the components of orbital planes' direction vector) satisfying the SO(3) algebra on a non-canonical phase space is induced by solely the effective potential energy term of VRR. For this dynamics, Roupas, Kocsis & Tremaine [48] identified gravitational phase transitions in VRR. They calculated the spacial distribution of orbital planes' orientation vectors at thermodynamic equilibrium. In this work, I will again apply the time-averaging method over the apsidal precession's timescale , but now on the full N-body Hamiltonian, with all kinetic terms consistently included. The resulting "rigid-body decomposition" of the effective energy accounts for three terms determining the evolution; namely, a rotational, normal kinetic term accounting for the orbital planes' precession and nutation, a spin kinetic term accounting for the in-plane rotation and the gravitational interaction term at quadrapole and higher order. This effective Hamiltonian describes rigid, disk-shaped, spinning tops allowed to rotate about any of their diameters crossing the common fixed centre, in direct analogy with rigid body dynamics [49] Torques on each disk develop due to mutual gravitational attraction. The general dynamical equations of motion of VRR are calculated in the rigid-body decomposition. They naturally induce new physical parameters, which connect the physical properties of the effective system (rigid annular disks) with these of the implicit system (orbiting point masses). These parameters are the moments of inertia and spin magnitudes of the effective rigid disks. They are connected with the averaging timescale and the ratio ε of the mass of the cluster to that of the central object. The gravitational couplings mediate the two views-implicit and effective-of the system and allow for such relations to emerge. The aforementioned SO(3) evolution induced by a zero kinetic term turns out to be the approximation of the special limit ε = 0 at zeroth order. More importantly, the identified relations between properties of the implicit and effective systems allow for the generalization of the dynamics and the validation and further generalization of the gravitational phase transitions in the cases that the clusters' mass is comparable to that of the central massive object. I specify the dynamical conditions for which such generalization may be valid. Last, but not least, I calculate the dependence of the dispersion of disks' precession and nutation on temperature. It depends on ε and moments of inertia in a non-trivial way. Due to the later dependence, it is possible that different families of bodies acquire different dispersions, even at orders of magnitude. Note that VRR resembles mathematically in certain aspects the Hamiltonian mean-field model (HMF) [50, 51] and the interested reader might find instructive the analogy. In the next section 2 I time-average the self-gravitating N-body Hamiltonian, demonstrate the equations of motion that emerge and calculate the boundaries of the effective, canonical phase space. In section 3 I develop in detail the statistical mechanics of the system. I formally define the microcanonical, the canonical and the Gibbs-canonical ensembles and consider a thermodynamic limit. In section 4, I discuss the inequivalence of ensmbles. In section 5 I review, validate and generalize the VRR gravitational phase transitions. In section 6 I inspect the kinetic energy term and calculate the dependence of the velocity dispersion on temperature. In section 7 I briefly modify the analysis to account for continuous rigid bodies. In the final section 8 I discuss the results.
Astronomy & Astrophysics, 2019
Supernova theory suggests that black holses of a stellar origin cannot attain masses in the range... more Supernova theory suggests that black holses of a stellar origin cannot attain masses in the range of 50−135 solar masses in isolation. We argue here that this mass gap is filled in by black holes that grow by gas accretion in dense stellar clusters, such as protoglobular clusters. The accretion proceeds rapidly, during the first 10 megayears of the cluster life, before the remnant gas is depleted. We predict that binaries of black holes within the mass gap can be observed by LIGO.
Classical and Quantum Gravity, 2019
We describe microcanonical phase transitions and instabilities of the ideal Fermi gas in general ... more We describe microcanonical phase transitions and instabilities of the ideal Fermi gas in general relativity at nonzero temperature confined in the interior of a spherical shell. The thermodynamic behaviour is governed by the compactness of rest mass, namely of the total rest mass over radius of the system. For a fixed value of rest mass compactness, we study the caloric curves as a function of the size of the spherical box. At low compactness values, low energies and for sufficiently big systems the system is subject to a gravothermal catastrophe, which cannot be halted by quantum degeneracy pressure, and the system collapses. For small systems, there appears no instability at low energies. For intermediate sizes, between two marginal values, gravothermal catastrophe is halted and a microcanonical phase transition occurs from a gaseous phase to a condensed phase with a nearly degenerate core. The system is subject to a relativistic instability at low energy, when the core gets sufficiently condensed above the Oppenheimer-Volkoff limit. For sufficiently high values of rest mass compactness the microcanonical phase transitions are suppressed. They are replaced either by an Antonov type gravothermal catastrophe for sufficiently big systems or by stable equilibria for small systems. At high energies the system is subject to the 'relativistic gravothermal instability', identified by Roupas in [1], for all values of compactness and any size. * This change of regime, here and in points (ii) and (iii) below, is due to the fact that the selfgravitating Fermi gas at T = 0 is confined by the box, instead of being self-confined, when the box radius is too small.
Universe, 2019
The gravitational instability, responsible for the formation of the structure of the Universe, oc... more The gravitational instability, responsible for the formation of the structure of the Universe, occurs below energy thresholds and above spatial scales of a self-gravitating expanding region, when thermal energy can no longer counterbalance self-gravity. I argue that at sufficiently-large scales, dark energy may restore thermal stability. This stability re-entrance of an isothermal sphere defines a turnaround radius, which dictates the maximum allowed size of any structure generated by gravitational instability. On the opposite limit of high energies and small scales, I will show that an ideal, quantum or classical, self-gravitating gas is subject to a high-energy relativistic gravothermal instability. It occurs at sufficiently-high energy and small radii, when thermal energy cannot support its own gravitational attraction. Applications of the phenomenon include neutron stars and core-collapse supernovae. I also extend the original Oppenheimer–Volkov calculation of the maximum mass l...
Astronomy & Astrophysics, 2019
We show that binaries of stellar-mass black holes formed inside a young protoglobular cluster, ca... more We show that binaries of stellar-mass black holes formed inside a young protoglobular cluster, can grow rapidly inside the cluster’s core by accretion of the intracluster gas, before the gas may be depleted from the core. A black hole with mass of the order of eight solar masses can grow to values of the order of thirty five solar masses in accordance with recent gravitational waves signals observed by LIGO. Due to the black hole mass increase, a binary may also harden. The growth of binary black holes in a dense protoglobular cluster through mass accretion indicates a potentially important formation and hardening channel.
The Astrophysical Journal, 2017
We examine dense self-gravitating stellar systems dominated by a central potential, such as nucle... more We examine dense self-gravitating stellar systems dominated by a central potential, such as nuclear star clusters hosting a central supermassive black hole. Different dynamical properties of these systems evolve on vastly different timescales. In particular, the orbital-plane orientations are typically driven into internal thermodynamic equilibrium by vector resonant relaxation before the orbital eccentricities or semimajor axes relax. We show that the statistical mechanics of such systems exhibit a striking resemblance to liquid crystals, with analogous ordered-nematic and disordered-isotropic phases. The ordered phase consists of bodies orbiting in a disk in both directions, with the disk thickness depending on temperature, while the disordered phase corresponds to a nearly isotropic distribution of the orbit normals. We show that below a critical value of the total angular momentum, the system undergoes a first-order phase transition between the ordered and disordered phases. At the critical point the phase transition becomes second-order while for higher angular momenta there is a smooth crossover. We also find metastable equilibria containing two identical disks with mutual inclinations between 90 • and 180 • .
Classical and Quantum Gravity, 2015
The thermodynamic instabilities of the self-gravitating, classical ideal gas are studied in the c... more The thermodynamic instabilities of the self-gravitating, classical ideal gas are studied in the case of static, spherically symmetric configurations in General Relativity taking into account the Tolman-Ehrenfest effect. One type of instabilities is found at low energies, where thermal energy becomes too weak to halt gravity and another at high energies, where gravitational attraction of thermal pressure overcomes its stabilizing effect. These turning points of stability are found to depend on the total rest mass M over the radius R. The low energy instability is the relativistic generalization of Antonov instability, which is recovered in the limit GM ≪ Rc 2 and low temperatures, while in the same limit and high temperatures, the high energy instability recovers the instability of the radiation equation of state. In the temperature versus energy diagram of series of equilibria, the two types of gravothermal instabilities make themselves evident as a double spiral! The two energy limits correspond also to radius limits. So that, stable static configurations exist only in between two marginal radii for any fixed energy with negative thermal plus gravitational energy. Ultimate limits of rest mass, as well as total mass-energy, are reported. Applications to neutron cores are discussed.
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Papers by Zacharias Roupas