The (first-order) gravitational self-force correction to the spin-orbit precession of a spinning ... more The (first-order) gravitational self-force correction to the spin-orbit precession of a spinning compact body along a slightly eccentric orbit around a Schwarzschild black hole is computed through the ninth post-Newtonian order, improving recent results by Kavanagh et al. [Phys. Rev. D 96, 064012 (2017).] This information is then converted into its corresponding Effective-One-Body counterpart, thereby determining several new post-Newtonian terms in the gyrogravitomagnetic ratio gS * .
We compute to high post-Newtonian accuracy the 4-momentum (linear momentum, and energy), radiated... more We compute to high post-Newtonian accuracy the 4-momentum (linear momentum, and energy), radiated as gravitational waves in a two-body system undergoing gravitational scattering. We include, for the first time, all the relevant time-asymmetric effects that arise when consistently going three post Newtonian orders beyond the leading post Newtonian order. We find that the inclusion of time-asymmetric radiative effects (both in tails and in the radiation-reacted hyperbolic motion) is crucial to ensure the mass-polynomiality of the post-Minkowskian expansion (G expansion) of the radiated 4-momentum. Imposing the mass-polynomiality of the corresponding individual impulses determines the conservativelike radiative contributions at the fourth post-Minkowskian order, and strongly constrains them at the fifth post-Minkowskian order. 1 We recall that the leading PN orders of radiative losses is the 2.5PN order for energy and angular momentum, while it is the 3.5PN order for linear momentum.
We investigate the hyperbolic scattering of test particles, spinning test particles and particles... more We investigate the hyperbolic scattering of test particles, spinning test particles and particles with spin-induced quadrupolar structure by a Kerr black hole in the ultrarelativistic regime. We also study how the features of the scattering process modify if the source of the background gravitational field is endowed with a nonzero mass quadrupole moment as described by the (approximate) Hartle-Thorne solution. We compute the scattering angle either in closed analytical form, when possible, or as a power series of the (dimensionless) inverse impact parameter. It is a function of the parameters characterizing the source (intrinsic angular momentum and mass quadrupole moment) as well as the scattered body (spin and polarizability constant). Measuring the scattering angle thus provides useful information to determine the nature of the two components of the binary system undergoing high-energy scattering processes.
We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession... more We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession along circular orbits in the Schwarzschild spacetime. In particular we present high order post-Newtonian expansions for the gauge invariant precession function along circular geodesics valid for arbitrary Kerr spin parameter and show agreement between these results and those derived from the full post-Newtonian conservative dynamics. Finally we present strong field numerical data for a range of the Kerr spin parameter, showing agreement with the GSF-PN results, and the expected lightring divergent behaviour. These results provide useful testing benchmarks for selfforce calculations in Kerr spacetime, and provide an avenue for translating self-force data into the spin-spin coupling in effective-one-body models.
We study the metric perturbations induced by a classical spinning particle moving along a circula... more We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the equatorial plane and has its spin aligned with the z-axis. The metric perturbations are obtained by using two different approaches, i.e., by working in two different gauges: the Regge-Wheeler gauge (using the Regge-Wheeler-Zerilli formalism) and a radiation gauge (using the Teukolsky formalism). We then compute the linear-in-spin contribution to the first-order self-force contribution to Detweiler's redshift invariant up to the 8.5 post-Newtonian order. We check that our result is the same in both gauges, as appropriate for a gauge-invariant quantity, and agrees with the currently known 3.5 post-Newtonian results.
We compute the rotations, during a scattering encounter, of the spins of two gravitationally inte... more We compute the rotations, during a scattering encounter, of the spins of two gravitationally interacting particles at second-order in the gravitational constant (second post-Minkowskian order). Following a strategy introduced in Phys. Rev. D 96, 104038 (2017), we transcribe our result into a correspondingly improved knowledge of the spin-orbit sector of the Effective One-Body (EOB) Hamiltonian description of the dynamics of spinning binary systems. We indicate ways of resumming our results for defining improved versions of spinning EOB codes which might help in providing a better analytical description of the dynamics of coalescing spinning binary black holes.
Test particle geodesic motion is analysed in detail for the background spacetimes of the degenera... more Test particle geodesic motion is analysed in detail for the background spacetimes of the degenerate Ferrari-Ibañez colliding gravitational wave solutions. Killing vectors have been used to reduce the equations of motion to a first order system of differential equations which have been integrated numerically. The associated constants of the motion have also been used to match the geodesics as they cross over the boundary between the single plane wave and interaction zones.
Gravitational perturbations of the de Sitter spacetime are investigated using the Regge-Wheeler f... more Gravitational perturbations of the de Sitter spacetime are investigated using the Regge-Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heuntype for both electric and magnetic multipoles. The solution so obtained is used to study the deviation from an initially radial geodesic due to the perturbation. The spectral properties of the perturbed metric are also analyzed. Finally, gaugeand tetrad-invariant first-order massless perturbations of any spin are explored following the approach of Teukolsky. The existence of closed-form, i.e. Liouvillian, solutions to the radial part of the Teukolsky master equation is discussed.
We compute the first-order self-force contribution to Detweiler's redshift invariant for extended... more We compute the first-order self-force contribution to Detweiler's redshift invariant for extended bodies endowed with both dipolar and quadrupolar structure (with spin-induced quadrupole moment) moving along circular orbits on a Schwarzschild background. Our analysis includes effects which are second order in spin, generalizing previous results for purely spinning particles. The perturbing body is assumed to move on the equatorial plane, the associated spin vector being orthogonal to it. The metric perturbations are obtained by using a standard gravitational self-force approach in a radiation gauge. Our results are accurate through the 6.5 post-Newtonian order, and are shown to reproduce the corresponding post-Newtonian expression for the same quantity computed by using the available Hamiltonian from an effective field theory approach for the dynamics of spinning binaries.
A single master equation is given describing spin s ≤ 2 test fields that are gauge-and tetradinva... more A single master equation is given describing spin s ≤ 2 test fields that are gauge-and tetradinvariant perturbations of the spinning C metric spacetime representing a source with mass M , uniformly rotating with angular momentum per unit mass a and uniformly accelerated with acceleration A. This equation can be separated into its radial and angular parts. The behavior of the radial functions near the horizons is studied and used to examine the influence of A on the phenomenon of superradiance, while the angular equation leads to modified spin-weighted spheroidal harmonic solutions generalizing those of the Kerr spacetime. Finally the coupling between the spin of the perturbing field and the acceleration parameter A is discussed.
Page 1. Gravitational waves, gyroscopes and frame dragging This article has been downloaded from ... more Page 1. Gravitational waves, gyroscopes and frame dragging This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2001 Class. Quantum Grav. 18 2945 (http://iopscience.iop.org/0264-9381/18/15/309) ...
Using a recently introduced method [Phys. Rev. Lett. 123, 231104 (2019)], which splits the conser... more Using a recently introduced method [Phys. Rev. Lett. 123, 231104 (2019)], which splits the conservative dynamics of gravitationally interacting binary systems into a non-local-in-time part and a local-in-time one, we compute the local part of the dynamics at the sixth post-Newtonian (6PN) accuracy. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, effective-field-theory, gravitational self-force, effective one-body, and Delaunay averaging. The full functional structure of the local 6PN Hamiltonian (which involves 151 numerical coefficients) is derived, but contains four undetermined numerical coefficients. Our 6PN-accurate results are complete at orders G 3 and G 4 , and the derived O(G 3) scattering angle agrees, within our 6PN accuracy, with the computation of [Phys. Rev. Lett. 122, no. 20, 201603 (2019)]. All our results are expressed in several different gauge-invariant ways. We highlight, and make a crucial use of, several aspects of the hidden simplicity of the mass-ratio dependence of the two-body dynamics.
The transformation laws of the relative local geometrical-kinematical features (velocity, acceler... more The transformation laws of the relative local geometrical-kinematical features (velocity, acceleration, angular and deformation velocities etc.) for a moving continuum, with respect to any change of galileian frame of reference, are reconsidered from a general point of view.
... spacetime have been" known" for quite some time thanks to their complete integrabil... more ... spacetime have been" known" for quite some time thanks to their complete integrability in ... the present remarks also apply to the wider class of orthogonally transitive stationary axisymmetric ... in the px coordi-nate plane of the corresponding flat spacetime cylindrical coordinates (p ...
The existence of Closed Timelike Curves (CTCs) in a generic spacetime is often associated with a ... more The existence of Closed Timelike Curves (CTCs) in a generic spacetime is often associated with a non-physical choice of coordinates and can be cured by limiting the admissibility of such coordinates. Lichnerowicz conditions, for instance, represent a criterion for admissibility. The result, however, is a very restrictive limitation which may imply "removal" of important regions (with respect to the peculiarity of phenomena which may happen there) of the spacetime manifold. We consider here the point of view of a family of observers (Fundamental Slicing Observers, FSO) having their world lines orthogonal to the surfaces of constant coordinate time. We say that the time coordinate has not a global character if the associated FSO change their causality condition in the domain of validity of the coordinates themselves. Furthermore, in those regions where FSO have no more timelike world lines, CTCs are present and one may think of special devices or investigation tools apt to operationally detect them. We will discuss in detail theoretical approaches involving (scalar) waves or photons.
In the description of the relativistic two-body interaction, together with the effects of energy ... more In the description of the relativistic two-body interaction, together with the effects of energy and angular momentum losses due to the emission of gravitational radiation, one has to take into account also the loss of linear momentum, which is responsible for the recoil of the center-of-mass of the system. We compute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to the linear momentum flux for a nonspinning binary system either along hyperboliclike or ellipticlike orbits. The corresponding orbital averages are evaluated at their leading post-Newtonian approximation, using harmonic coordinates and working in the Fourier domain. The final expressions are given in a large-eccentricity (or large-angular momentum) expansion along hyperboliclike orbits and in a small-eccentricity expansion along ellipticlike orbits. We thus complete a previous analysis focusing on both energy and angular momentum losses [Phys. Rev. D 104, no.10, 104020 (2021)], providing brick-type results which will be useful, e.g., in the high-accurate determination of the radiated impulses of the two bodies undergoing a scattering process.
The (first-order) gravitational self-force correction to the spin-orbit precession of a spinning ... more The (first-order) gravitational self-force correction to the spin-orbit precession of a spinning compact body along a slightly eccentric orbit around a Schwarzschild black hole is computed through the ninth post-Newtonian order, improving recent results by Kavanagh et al. [Phys. Rev. D 96, 064012 (2017).] This information is then converted into its corresponding Effective-One-Body counterpart, thereby determining several new post-Newtonian terms in the gyrogravitomagnetic ratio gS * .
We compute to high post-Newtonian accuracy the 4-momentum (linear momentum, and energy), radiated... more We compute to high post-Newtonian accuracy the 4-momentum (linear momentum, and energy), radiated as gravitational waves in a two-body system undergoing gravitational scattering. We include, for the first time, all the relevant time-asymmetric effects that arise when consistently going three post Newtonian orders beyond the leading post Newtonian order. We find that the inclusion of time-asymmetric radiative effects (both in tails and in the radiation-reacted hyperbolic motion) is crucial to ensure the mass-polynomiality of the post-Minkowskian expansion (G expansion) of the radiated 4-momentum. Imposing the mass-polynomiality of the corresponding individual impulses determines the conservativelike radiative contributions at the fourth post-Minkowskian order, and strongly constrains them at the fifth post-Minkowskian order. 1 We recall that the leading PN orders of radiative losses is the 2.5PN order for energy and angular momentum, while it is the 3.5PN order for linear momentum.
We investigate the hyperbolic scattering of test particles, spinning test particles and particles... more We investigate the hyperbolic scattering of test particles, spinning test particles and particles with spin-induced quadrupolar structure by a Kerr black hole in the ultrarelativistic regime. We also study how the features of the scattering process modify if the source of the background gravitational field is endowed with a nonzero mass quadrupole moment as described by the (approximate) Hartle-Thorne solution. We compute the scattering angle either in closed analytical form, when possible, or as a power series of the (dimensionless) inverse impact parameter. It is a function of the parameters characterizing the source (intrinsic angular momentum and mass quadrupole moment) as well as the scattered body (spin and polarizability constant). Measuring the scattering angle thus provides useful information to determine the nature of the two components of the binary system undergoing high-energy scattering processes.
We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession... more We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession along circular orbits in the Schwarzschild spacetime. In particular we present high order post-Newtonian expansions for the gauge invariant precession function along circular geodesics valid for arbitrary Kerr spin parameter and show agreement between these results and those derived from the full post-Newtonian conservative dynamics. Finally we present strong field numerical data for a range of the Kerr spin parameter, showing agreement with the GSF-PN results, and the expected lightring divergent behaviour. These results provide useful testing benchmarks for selfforce calculations in Kerr spacetime, and provide an avenue for translating self-force data into the spin-spin coupling in effective-one-body models.
We study the metric perturbations induced by a classical spinning particle moving along a circula... more We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the equatorial plane and has its spin aligned with the z-axis. The metric perturbations are obtained by using two different approaches, i.e., by working in two different gauges: the Regge-Wheeler gauge (using the Regge-Wheeler-Zerilli formalism) and a radiation gauge (using the Teukolsky formalism). We then compute the linear-in-spin contribution to the first-order self-force contribution to Detweiler's redshift invariant up to the 8.5 post-Newtonian order. We check that our result is the same in both gauges, as appropriate for a gauge-invariant quantity, and agrees with the currently known 3.5 post-Newtonian results.
We compute the rotations, during a scattering encounter, of the spins of two gravitationally inte... more We compute the rotations, during a scattering encounter, of the spins of two gravitationally interacting particles at second-order in the gravitational constant (second post-Minkowskian order). Following a strategy introduced in Phys. Rev. D 96, 104038 (2017), we transcribe our result into a correspondingly improved knowledge of the spin-orbit sector of the Effective One-Body (EOB) Hamiltonian description of the dynamics of spinning binary systems. We indicate ways of resumming our results for defining improved versions of spinning EOB codes which might help in providing a better analytical description of the dynamics of coalescing spinning binary black holes.
Test particle geodesic motion is analysed in detail for the background spacetimes of the degenera... more Test particle geodesic motion is analysed in detail for the background spacetimes of the degenerate Ferrari-Ibañez colliding gravitational wave solutions. Killing vectors have been used to reduce the equations of motion to a first order system of differential equations which have been integrated numerically. The associated constants of the motion have also been used to match the geodesics as they cross over the boundary between the single plane wave and interaction zones.
Gravitational perturbations of the de Sitter spacetime are investigated using the Regge-Wheeler f... more Gravitational perturbations of the de Sitter spacetime are investigated using the Regge-Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heuntype for both electric and magnetic multipoles. The solution so obtained is used to study the deviation from an initially radial geodesic due to the perturbation. The spectral properties of the perturbed metric are also analyzed. Finally, gaugeand tetrad-invariant first-order massless perturbations of any spin are explored following the approach of Teukolsky. The existence of closed-form, i.e. Liouvillian, solutions to the radial part of the Teukolsky master equation is discussed.
We compute the first-order self-force contribution to Detweiler's redshift invariant for extended... more We compute the first-order self-force contribution to Detweiler's redshift invariant for extended bodies endowed with both dipolar and quadrupolar structure (with spin-induced quadrupole moment) moving along circular orbits on a Schwarzschild background. Our analysis includes effects which are second order in spin, generalizing previous results for purely spinning particles. The perturbing body is assumed to move on the equatorial plane, the associated spin vector being orthogonal to it. The metric perturbations are obtained by using a standard gravitational self-force approach in a radiation gauge. Our results are accurate through the 6.5 post-Newtonian order, and are shown to reproduce the corresponding post-Newtonian expression for the same quantity computed by using the available Hamiltonian from an effective field theory approach for the dynamics of spinning binaries.
A single master equation is given describing spin s ≤ 2 test fields that are gauge-and tetradinva... more A single master equation is given describing spin s ≤ 2 test fields that are gauge-and tetradinvariant perturbations of the spinning C metric spacetime representing a source with mass M , uniformly rotating with angular momentum per unit mass a and uniformly accelerated with acceleration A. This equation can be separated into its radial and angular parts. The behavior of the radial functions near the horizons is studied and used to examine the influence of A on the phenomenon of superradiance, while the angular equation leads to modified spin-weighted spheroidal harmonic solutions generalizing those of the Kerr spacetime. Finally the coupling between the spin of the perturbing field and the acceleration parameter A is discussed.
Page 1. Gravitational waves, gyroscopes and frame dragging This article has been downloaded from ... more Page 1. Gravitational waves, gyroscopes and frame dragging This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2001 Class. Quantum Grav. 18 2945 (http://iopscience.iop.org/0264-9381/18/15/309) ...
Using a recently introduced method [Phys. Rev. Lett. 123, 231104 (2019)], which splits the conser... more Using a recently introduced method [Phys. Rev. Lett. 123, 231104 (2019)], which splits the conservative dynamics of gravitationally interacting binary systems into a non-local-in-time part and a local-in-time one, we compute the local part of the dynamics at the sixth post-Newtonian (6PN) accuracy. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, effective-field-theory, gravitational self-force, effective one-body, and Delaunay averaging. The full functional structure of the local 6PN Hamiltonian (which involves 151 numerical coefficients) is derived, but contains four undetermined numerical coefficients. Our 6PN-accurate results are complete at orders G 3 and G 4 , and the derived O(G 3) scattering angle agrees, within our 6PN accuracy, with the computation of [Phys. Rev. Lett. 122, no. 20, 201603 (2019)]. All our results are expressed in several different gauge-invariant ways. We highlight, and make a crucial use of, several aspects of the hidden simplicity of the mass-ratio dependence of the two-body dynamics.
The transformation laws of the relative local geometrical-kinematical features (velocity, acceler... more The transformation laws of the relative local geometrical-kinematical features (velocity, acceleration, angular and deformation velocities etc.) for a moving continuum, with respect to any change of galileian frame of reference, are reconsidered from a general point of view.
... spacetime have been" known" for quite some time thanks to their complete integrabil... more ... spacetime have been" known" for quite some time thanks to their complete integrability in ... the present remarks also apply to the wider class of orthogonally transitive stationary axisymmetric ... in the px coordi-nate plane of the corresponding flat spacetime cylindrical coordinates (p ...
The existence of Closed Timelike Curves (CTCs) in a generic spacetime is often associated with a ... more The existence of Closed Timelike Curves (CTCs) in a generic spacetime is often associated with a non-physical choice of coordinates and can be cured by limiting the admissibility of such coordinates. Lichnerowicz conditions, for instance, represent a criterion for admissibility. The result, however, is a very restrictive limitation which may imply "removal" of important regions (with respect to the peculiarity of phenomena which may happen there) of the spacetime manifold. We consider here the point of view of a family of observers (Fundamental Slicing Observers, FSO) having their world lines orthogonal to the surfaces of constant coordinate time. We say that the time coordinate has not a global character if the associated FSO change their causality condition in the domain of validity of the coordinates themselves. Furthermore, in those regions where FSO have no more timelike world lines, CTCs are present and one may think of special devices or investigation tools apt to operationally detect them. We will discuss in detail theoretical approaches involving (scalar) waves or photons.
In the description of the relativistic two-body interaction, together with the effects of energy ... more In the description of the relativistic two-body interaction, together with the effects of energy and angular momentum losses due to the emission of gravitational radiation, one has to take into account also the loss of linear momentum, which is responsible for the recoil of the center-of-mass of the system. We compute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to the linear momentum flux for a nonspinning binary system either along hyperboliclike or ellipticlike orbits. The corresponding orbital averages are evaluated at their leading post-Newtonian approximation, using harmonic coordinates and working in the Fourier domain. The final expressions are given in a large-eccentricity (or large-angular momentum) expansion along hyperboliclike orbits and in a small-eccentricity expansion along ellipticlike orbits. We thus complete a previous analysis focusing on both energy and angular momentum losses [Phys. Rev. D 104, no.10, 104020 (2021)], providing brick-type results which will be useful, e.g., in the high-accurate determination of the radiated impulses of the two bodies undergoing a scattering process.
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