400 research outputs found
On the Effect of Constraint Enforcement on the Quality of Numerical Solutions in General Relativity
In Brodbeck et al 1999 it has been shown that the linearised time evolution
equations of general relativity can be extended to a system whose solutions
asymptotically approach solutions of the constraints. In this paper we extend
the non-linear equations in similar ways and investigate the effect of various
possibilities by numerical means. Although we were not able to make the
constraint submanifold an attractor for all solutions of the extended system,
we were able to significantly reduce the growth of the numerical violation of
the constraints. Contrary to our expectations this improvement did not imply a
numerical solution closer to the exact solution, and therefore did not improve
the quality of the numerical solution.Comment: 14 pages, 9 figures, accepted for publication in Phys. Rev.
Self-force of a scalar field for circular orbits about a Schwarzschild black hole
The foundations are laid for the numerical computation of the actual
worldline for a particle orbiting a black hole and emitting gravitational
waves. The essential practicalities of this computation are here illustrated
for a scalar particle of infinitesimal size and small but finite scalar charge.
This particle deviates from a geodesic because it interacts with its own
retarded field \psi^\ret. A recently introduced Green's function G^\SS
precisely determines the singular part, \psi^\SS, of the retarded field. This
part exerts no force on the particle. The remainder of the field \psi^\R =
\psi^\ret - \psi^\SS is a vacuum solution of the field equation and is
entirely responsible for the self-force. A particular, locally inertial
coordinate system is used to determine an expansion of \psi^\SS in the
vicinity of the particle. For a particle in a circular orbit in the
Schwarzschild geometry, the mode-sum decomposition of the difference between
\psi^\ret and the dominant terms in the expansion of \psi^\SS provide a
mode-sum decomposition of an approximation for from which the
self-force is obtained. When more terms are included in the expansion, the
approximation for is increasingly differentiable, and the mode-sum
for the self-force converges more rapidly.Comment: RevTex, 31 pages, 1 figure, modified abstract, more details of
numerical method
Radiation reaction and energy-momentum conservation
We discuss subtle points of the momentum balance for radiating particles in
flat and curved space-time. An instantaneous balance is obscured by the
presence of the Schott term which is a finite part of the bound field momentum.
To establish the balance one has to take into account the initial and final
conditions for acceleration, or to apply averaging. In curved space-time an
additional contribution arises from the tidal deformation of the bound field.
This force is shown to be the finite remnant from the mass renormalization and
it is different both form the radiation recoil force and the Schott force. For
radiation of non-gravitational nature from point particles in curved space-time
the reaction force can be computed substituting the retarded field directly to
the equations of motion. Similar procedure is applicable to gravitational
radiation in vacuum space-time, but fails in the non-vacuum case. The existence
of the gravitational quasilocal reaction force in this general case seems
implausible, though it still exists in the non-relativistic approximation. We
also explain the putative antidamping effect for gravitational radiation under
non-geodesic motion and derive the non-relativistic gravitational quadrupole
Schott term. Radiation reaction in curved space of dimension other than four is
also discussedComment: Lecture given at the C.N.R.S. School "Mass and Motion in General
Relativity", Orleans, France, 200
Canonical Quantization of the Electromagnetic Field on the Kerr Background
We investigate the canonical quantization of the electromagnetic field on the
Kerr background. We give new expressions for the expectation value of the
electromagnetic stress-energy tensor in various vacua states and give a
physical interpretation of the separate terms appearing in them. We numerically
calculate the luminosity in these states. We also study the form of the
renormalized stress-energy tensor close to the horizon when the electromagnetic
field is in the past Boulware state.Comment: 27 zipped, postscript figure file
The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2
We study the near horizon limit of a four dimensional extreme rotating black
hole. The limiting metric is a completely nonsingular vacuum solution, with an
enhanced symmetry group SL(2,R) x U(1). We show that many of the properties of
this solution are similar to the AdS_2 x S^2 geometry arising in the near
horizon limit of extreme charged black holes. In particular, the boundary at
infinity is a timelike surface. This suggests the possibility of a dual quantum
mechanical description. A five dimensional generalization is also discussed.Comment: 21 page
Quasinormal resonances of a massive scalar field in a near-extremal Kerr black hole spacetime
The fundamental resonances of near-extremal Kerr black holes due to massive
scalar perturbations are derived {\it analytically}. We show that there exists
a critical mass parameter, , below which increasing the mass of
the field increases the oscillation frequency of the resonance.
On the other hand, above the critical field mass increasing the mass
increases the damping rate of the mode. We confirm our analytical
results by numerical computations.Comment: 6 page
Scattering of gravitational radiation: second order moments of the wave amplitude
Gravitational radiation that propagates through an inhomogeneous mass
distribution is subject to random gravitational lensing, or scattering, causing
variations in the wave amplitude and temporal smearing of the signal. A
statistical theory is constructed to treat these effects. The statistical
properties of the wave amplitude variations are a direct probe of the power
spectrum of the mass distribution through which the waves propagate. Scattering
temporally smears any intensity variations intrinsic to a source emitting
gravitational radiation, rendering variability on time scales shorter than the
temporal smearing time scale unobservable, and potentially making the radiation
much harder to detect. Gravitational radiation must propagate out through the
mass distribution of its host galaxy before it can be detected at the Earth.
Plausible models for the distribution of matter in an host galaxy suggest
that the temporal smearing time scale is at least several milliseconds due to
the gas content alone, and may be as large as a second if dark matter also
scatters the radiation. The smearing time due to scattering by any galaxy
interposed along the line of sight is a factor times larger.
Gravitational scattering is an excellent probe of matter on parsec and
sub-parsec scales, and has the potential to elucidate the nature of dark
matter.Comment: A&A accepted, 19 pages, 4 fig
Regularization of the Teukolsky Equation for Rotating Black Holes
We show that the radial Teukolsky equation (in the frequency domain) with
sources that extend to infinity has well-behaved solutions. To prove that, we
follow Poisson approach to regularize the non-rotating hole, and extend it to
the rotating case. To do so we use the Chandrasekhar transformation among the
Teukolsky and Regge-Wheeler-like equations, and express the integrals over the
source in terms of solutions to the homogeneous Regge-Wheeler-like equation, to
finally regularize the resulting integral. We then discuss the applicability of
these results.Comment: 14 pages, 1 Table, REVTE
The scalar perturbation of the higher-dimensional rotating black holes
The massless scalar field in the higher-dimensional Kerr black hole (Myers-
Perry solution with a single rotation axis) has been investigated. It has been
shown that the field equation is separable in arbitrary dimensions. The
quasi-normal modes of the scalar field have been searched in five dimensions
using the continued fraction method. The numerical result shows the evidence
for the stability of the scalar perturbation of the five-dimensional Kerr black
holes. The time scale of the resonant oscillation in the rapidly rotating black
hole, in which case the horizon radius becomes small, is characterized by
(black hole mass)^{1/2}(Planck mass)^{-3/2} rather than the light-crossing time
of the horizon.Comment: 16 pages, 7 figures, revised versio
The radial infall of a highly relativistic point particle into a Kerr black hole along the symmetry axis
In this Letter we consider the radial infall along the symmetry axis of an
ultra-relativistic point particle into a rotating Kerr black hole. We use the
Sasaki-Nakamura formalism to compute the waveform, energy spectra and total
energy radiated during this process. We discuss possible connections between
these results and the black hole-black hole collision at the speed of light
process.Comment: 1 figur
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