523 research outputs found
A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit
We obtain a fourth order accurate numerical algorithm to integrate the
Zerilli and Regge-Wheeler wave equations, describing perturbations of
nonrotating black holes, with source terms due to an orbiting particle. Those
source terms contain the Dirac's delta and its first derivative. We also
re-derive the source of the Zerilli and Regge-Wheeler equations for more
convenient definitions of the waveforms, that allow direct metric
reconstruction (in the Regge-Wheeler gauge).Comment: 30 pages, 12 figure
Exact Gravitational Shock Wave Solution of Higher Order Theories
We find an {\it exact} pp--gravitational wave solution of the fourth order
gravity field equations. Outside the (delta--like) source this {\it not} a
vacuum solution of General Relativity. It represents the contribution of the
massive, , spin--two field associated to the Ricci squared
term in the gravitational Lagrangian. The fourth order terms tend to make
milder the singularity of the curvature at the point where the particle is
located. We generalize this analysis to --dimensions, extended sources, and
higher than fourth order theories. We also briefly discuss the scattering of
fields by this kind of plane gravitational waves.Comment: 12 pages, REVTEX, Fully revised version. Amplitude of the wave
computed. Discussion section added. Figure added. To appear in Phys. Rev.
Regular second order perturbations of binary black holes: The extreme mass ratio regime
In order to derive the precise gravitational waveforms for extreme mass ratio
inspirals (EMRI), we develop a formulation for the second order metric
perturbations produced by a point particle moving in the Schwarzschild
spacetime. The second order waveforms satisfy a wave equation with an effective
source build up from products of the first order perturbations and its
derivatives. We have explicitly regularized this source at the horizon and at
spatial infinity. We show that the effective source does not contain squares of
the Dirac's delta and that perturbations are regular at the particle location.
We introduce an asymptotically flat gauge for the radiation fields and the
mode to compute explicitly the (leading) second order
waveforms in the headon collision case. This case represents the first
completion of the radiation reaction program self-consistently.Comment: 28 pages, no figur
String Propagation through a Big Crunch/Big Bang Transition
We consider the propagation of classical and quantum strings on cosmological
space-times which interpolate from a collapsing phase to an expanding phase. We
begin by considering the classical propagation of strings on space-times with
isotropic and anisotropic cosmological singularities. We find that cosmological
singularities fall into two classes, in the first class the string evolution is
well behaved all the way up to the singularity, whilst in the second class it
becomes ill-defined. Then assuming the singularities are regulated by string
scale corrections, we consider the implications of the propagation through a
`bounce'. It is known that as we evolve through a bounce, quantum strings will
become excited giving rise to `particle transmutation'. We reconsider this
effect, giving qualitative arguments for the amount of excitation for each
class. We find that strings whose physical wavelength at the bounce is less
that inevitably emerge in highly excited states, and that in
this regime there is an interesting correspondence between strings on
anisotropic cosmological space-times and plane waves. We argue that long
wavelength modes, such as those describing cosmological perturbations, will
also emerge in mildly excited string scale mass states. Finally we discuss the
relevance of this to the propagation of cosmological perturbations in models
such as the ekpyrotic/cyclic universe.Comment: 15 page
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
Perspective on gravitational self-force analyses
A point particle of mass moving on a geodesic creates a perturbation
, of the spacetime metric , that diverges at the particle.
Simple expressions are given for the singular part of and its
distortion caused by the spacetime. This singular part h^\SS_{ab} is
described in different coordinate systems and in different gauges. Subtracting
h^\SS_{ab} from leaves a regular remainder . The
self-force on the particle from its own gravitational field adjusts the world
line at \Or(\mu) to be a geodesic of ; this adjustment
includes all of the effects of radiation reaction. For the case that the
particle is a small non-rotating black hole, we give a uniformly valid
approximation to a solution of the Einstein equations, with a remainder of
\Or(\mu^2) as .
An example presents the actual steps involved in a self-force calculation.
Gauge freedom introduces ambiguity in perturbation analysis. However,
physically interesting problems avoid this ambiguity.Comment: 40 pages, to appear in a special issue of CQG on radiation reaction,
contains additional references, improved notation for tensor harmonic
Radiation content of Conformally flat initial data
We study the radiation of energy and linear momentum emitted to infinity by
the headon collision of binary black holes, starting from rest at a finite
initial separation, in the extreme mass ratio limit. For these configurations
we identify the radiation produced by the initially conformally flat choice of
the three geometry. This identification suggests that the radiated energy and
momentum of headon collisions will not be dominated by the details of the
initial data for evolution of holes from initial proper separations
. For non-headon orbits, where the amount of radiation is orders of
magnitude larger, the conformally flat initial data may provide a relative even
better approximation.Comment: 4 pages, 4 figure
String dynamics near a Kaluza-Klein black hole
The dynamics of a string near a Kaluza-Klein black hole are studied.
Solutions to the classical string equations of motion are obtained using the
world sheet velocity of light as an expansion parameter. The electrically and
magnetically charged cases are considered separately. Solutions for string
coordinates are obtained in terms of the world-sheet coordinate . It is
shown that the Kaluza-Klein radius increases/decreases with for
electrically/magnetically charged black hole.Comment: Latex2e file with six postscript figures. Minor changes, more
accurate numerical results and updated reference
Accurate black hole evolutions by fourth-order numerical relativity
We present techniques for successfully performing numerical relativity
simulations of binary black holes with fourth-order accuracy. Our simulations
are based on a new coding framework which currently supports higher order
finite differencing for the BSSN formulation of Einstein's equations, but which
is designed to be readily applicable to a broad class of formulations. We apply
our techniques to a standard set of numerical relativity test problems,
demonstrating the fourth-order accuracy of the solutions. Finally we apply our
approach to binary black hole head-on collisions, calculating the waveforms of
gravitational radiation generated and demonstrating significant improvements in
waveform accuracy over second-order methods with typically achievable numerical
resolution.Comment: 17 pages, 25 figure
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