1,157 research outputs found
Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field
We examine the motion in Schwarzschild spacetime of a point particle endowed
with a scalar charge. The particle produces a retarded scalar field which
interacts with the particle and influences its motion via the action of a
self-force. We exploit the spherical symmetry of the Schwarzschild spacetime
and decompose the scalar field in spherical-harmonic modes. Although each mode
is bounded at the position of the particle, a mode-sum evaluation of the
self-force requires regularization because the sum does not converge: the
retarded field is infinite at the position of the particle. The regularization
procedure involves the computation of regularization parameters, which are
obtained from a mode decomposition of the Detweiler-Whiting singular field;
these are subtracted from the modes of the retarded field, and the result is a
mode-sum that converges to the actual self-force. We present such a computation
in this paper. There are two main aspects of our work that are new. First, we
define the regularization parameters as scalar quantities by referring them to
a tetrad decomposition of the singular field. Second, we calculate four sets of
regularization parameters (denoted schematically by A, B, C, and D) instead of
the usual three (A, B, and C). As proof of principle that our methods are
reliable, we calculate the self-force acting on a scalar charge in circular
motion around a Schwarzschild black hole, and compare our answers with those
recorded in the literature.Comment: 38 pages, 2 figure
Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation
The first objective of this work is to obtain practical prescriptions to
calculate the absorption of mass and angular momentum by a black hole when
external processes produce gravitational radiation. These prescriptions are
formulated in the time domain within the framework of black-hole perturbation
theory. Two such prescriptions are presented. The first is based on the
Teukolsky equation and it applies to general (rotating) black holes. The second
is based on the Regge-Wheeler and Zerilli equations and it applies to
nonrotating black holes. The second objective of this work is to apply the
time-domain absorption formalisms to situations in which the black hole is
either small or slowly moving. In the context of this small-hole/slow-motion
approximation, the equations of black-hole perturbation theory can be solved
analytically, and explicit expressions can be obtained for the absorption of
mass and angular momentum. The changes in the black-hole parameters can then be
understood in terms of an interaction between the tidal gravitational fields
supplied by the external universe and the hole's tidally-induced mass and
current quadrupole moments. For a nonrotating black hole the quadrupole moments
are proportional to the rate of change of the tidal fields on the hole's world
line. For a rotating black hole they are proportional to the tidal fields
themselves.Comment: 36 pages, revtex4, no figures, final published versio
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
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
Quasi-local contribution to the scalar self-force: Geodesic Motion
We consider a scalar charge travelling in a curved background spacetime. We
calculate the quasi-local contribution to the scalar self-force experienced by
such a particle following a geodesic in a general spacetime. We also show that
if we assume a massless field and a vacuum background spacetime, the expression
for the self-force simplifies significantly. We consider some specific cases
whose gravitational analog are of immediate physical interest for the
calculation of radiation reaction corrected orbits of binary black hole
systems. These systems are expected to be detectable by the LISA space based
gravitational wave observatory. We also investigate how alternate techniques
may be employed in some specific cases and use these as a check on our own
results.Comment: Final Phys. Rev. D version. 24 pages, revtex4. Minor typos correcte
Gravitational waveforms from a point particle orbiting a Schwarzschild black hole
We numerically solve the inhomogeneous Zerilli-Moncrief and Regge-Wheeler
equations in the time domain. We obtain the gravitational waveforms produced by
a point-particle of mass traveling around a Schwarzschild black hole of
mass M on arbitrary bound and unbound orbits. Fluxes of energy and angular
momentum at infinity and the event horizon are also calculated. Results for
circular orbits, selected cases of eccentric orbits, and parabolic orbits are
presented. The numerical results from the time-domain code indicate that, for
all three types of orbital motion, black hole absorption contributes less than
1% of the total flux, so long as the orbital radius r_p(t) satisfies r_p(t)> 5M
at all times.Comment: revtex4, 24 pages, 23 figures, 3 tables, submitted to PR
Simulations of Extreme-Mass-Ratio Inspirals Using Pseudospectral Methods
Extreme-mass-ratio inspirals (EMRIs), stellar-mass compact objects (SCOs)
inspiralling into a massive black hole, are one of the main sources of
gravitational waves expected for the Laser Interferometer Space Antenna (LISA).
To extract the EMRI signals from the expected LISA data stream, which will also
contain the instrumental noise as well as other signals, we need very accurate
theoretical templates of the gravitational waves that they produce. In order to
construct those templates we need to account for the gravitational
backreaction, that is, how the gravitational field of the SCO affects its own
trajectory. In general relativity, the backreaction can be described in terms
of a local self-force, and the foundations to compute it have been laid
recently. Due to its complexity, some parts of the calculation of the
self-force have to be performed numerically. Here, we report on an ongoing
effort towards the computation of the self-force based on time-domain
multi-grid pseudospectral methods.Comment: 6 pages, 4 figures, JPCS latex style. Submitted to JPCS (special
issue for the proceedings of the 7th International LISA Symposium
A matched expansion approach to practical self-force calculations
We discuss a practical method to compute the self-force on a particle moving
through a curved spacetime. This method involves two expansions to calculate
the self-force, one arising from the particle's immediate past and the other
from the more distant past. The expansion in the immediate past is a covariant
Taylor series and can be carried out for all geometries. The more distant
expansion is a mode sum, and may be carried out in those cases where the wave
equation for the field mediating the self-force admits a mode expansion of the
solution. In particular, this method can be used to calculate the gravitational
self-force for a particle of mass mu orbiting a black hole of mass M to order
mu^2, provided mu/M << 1. We discuss how to use these two expansions to
construct a full self-force, and in particular investigate criteria for
matching the two expansions. As with all methods of computing self-forces for
particles moving in black hole spacetimes, one encounters considerable
technical difficulty in applying this method; nevertheless, it appears that the
convergence of each series is good enough that a practical implementation may
be plausible.Comment: IOP style, 8 eps figures, accepted for publication in a special issue
of Classical and Quantum Gravit
Light-cone coordinates based at a geodesic world line
Continuing work initiated in an earlier publication [Phys. Rev. D 69, 084007
(2004)], we construct a system of light-cone coordinates based at a geodesic
world line of an arbitrary curved spacetime. The construction involves (i) an
advanced-time or a retarded-time coordinate that labels past or future light
cones centered on the world line, (ii) a radial coordinate that is an affine
parameter on the null generators of these light cones, and (iii) angular
coordinates that are constant on each generator. The spacetime metric is
calculated in the light-cone coordinates, and it is expressed as an expansion
in powers of the radial coordinate in terms of the irreducible components of
the Riemann tensor evaluated on the world line. The formalism is illustrated in
two simple applications, the first involving a comoving world line of a
spatially-flat cosmology, the other featuring an observer placed on the axis of
symmetry of Melvin's magnetic universe.Comment: 11 pages, 1 figur
Quasi-local contribution to the scalar self-force: Non-geodesic Motion
We extend our previous calculation of the quasi-local contribution to the
self-force on a scalar particle to general (not necessarily geodesic) motion in
a general spacetime. In addition to the general case and the case of a particle
at rest in a stationary spacetime, we consider as examples a particle held at
rest in Reissner-Nordstrom and Kerr-Newman space-times. This allows us to most
easily analyse the effect of non-geodesic motion on our previous results and
also allows for comparison to existing results for Schwarzschild spacetime.Comment: 11 pages, 1 figure, corrected typo in Eq. 2.
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