2,160 research outputs found
Regularization of static self-forces
Various regularization methods have been used to compute the self-force
acting on a static particle in a static, curved spacetime. Many of these are
based on Hadamard's two-point function in three dimensions. On the other hand,
the regularization method that enjoys the best justification is that of
Detweiler and Whiting, which is based on a four-dimensional Green's function.
We establish the connection between these methods and find that they are all
equivalent, in the sense that they all lead to the same static self-force. For
general static spacetimes, we compute local expansions of the Green's functions
on which the various regularization methods are based. We find that these agree
up to a certain high order, and conjecture that they might be equal to all
orders. We show that this equivalence is exact in the case of ultrastatic
spacetimes. Finally, our computations are exploited to provide regularization
parameters for a static particle in a general static and spherically-symmetric
spacetime.Comment: 23 pages, no figure
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
Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force
The innermost stable circular orbit (ISCO) delimits the transition from
circular orbits to those that plunge into a black hole. In the test-mass limit,
well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes.
In the finite-mass case, there are a large variety of ways to define an ISCO in
a post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCO
condition of Blanchet & Iyer (2003) to the case of spinning (nonprecessing)
binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpected
properties: (1) it exactly reproduces the Schwarzschild ISCO in the test-mass
limit, and (2) it accurately approximates the recently-calculated shift in the
Schwarzschild ISCO frequency due to the conservative-piece of the gravitational
self-force [Barack & Sago (2009)]. The generalization of this ISCO condition to
spinning binaries has the property that it also exactly reproduces the Kerr
ISCO in the test-mass limit (up to the order at which PN spin corrections are
currently known). The shift in the ISCO due to the spin of the test-particle is
also calculated. Remarkably, the gauge-invariant PN ISCO condition exactly
reproduces the ISCO shift predicted by the Papapetrou equations for a
fully-relativistic spinning particle. It is surprising that an analysis of the
stability of the standard PN equations of motion is able (without any form of
"resummation") to accurately describe strong-field effects of the Kerr
spacetime. The ISCO frequency shift due to the conservative self-force in Kerr
is also calculated from this new ISCO condition, as well as from the
effective-one-body Hamiltonian of Barausse & Buonanno (2010). These results
serve as a useful point-of-comparison for future gravitational self-force
calculations in the Kerr spacetime.Comment: 17 pages, 2 figures, 1 table. v2: references added; minor changes to
match published versio
Self-forced gravitational waveforms for Extreme and Intermediate mass ratio inspirals
We present the first orbit-integrated self force effects on the gravitational
waveform for an I(E)MRI source. We consider the quasi-circular motion of a
particle in the spacetime of a Schwarzschild black hole and study the
dependence of the dephasing of the corresponding gravitational waveforms due to
ignoring the conservative piece of the self force. We calculate the cumulative
dephasing of the waveforms and their overlap integral, and discuss the
importance of the conservative piece of the self force in detection and
parameter estimation. For long templates the inclusion of the conservative
piece is crucial for gravitational-wave astronomy, yet may be ignored for short
templates with little effect on detection rate. We then discuss the effect of
the mass ratio and the start point of the motion on the dephasing.Comment: 9 pages, 15 figures. Substantially expanded and revised. We added:
description of the orbits and analysis of the dependence of the dephasing
effect on the parameter space, specifically the mass ratio and starting point
of the motion. Also added a more thorough description of out metho
The thermodynamic structure of Einstein tensor
We analyze the generic structure of Einstein tensor projected onto a 2-D
spacelike surface S defined by unit timelike and spacelike vectors u_i and n_i
respectively, which describe an accelerated observer (see text). Assuming that
flow along u_i defines an approximate Killing vector X_i, we then show that
near the corresponding Rindler horizon, the flux j_a=G_ab X^b along the ingoing
null geodesics k_i normalised to have unit Killing energy, given by j . k, has
a natural thermodynamic interpretation. Moreover, change in cross-sectional
area of the k_i congruence yields the required change in area of S under
virtual displacements \emph{normal} to it. The main aim of this note is to
clearly demonstrate how, and why, the content of Einstein equations under such
horizon deformations, originally pointed out by Padmanabhan, is essentially
different from the result of Jacobson, who employed the so called Clausius
relation in an attempt to derive Einstein equations from such a Clausius
relation. More specifically, we show how a \emph{very specific geometric term}
[reminiscent of Hawking's quasi-local expression for energy of spheres]
corresponding to change in \emph{gravitational energy} arises inevitably in the
first law: dE_G/d{\lambda} \alpha \int_{H} dA R_(2) (see text) -- the
contribution of this purely geometric term would be missed in attempts to
obtain area (and hence entropy) change by integrating the Raychaudhuri
equation.Comment: added comments and references; matches final version accepted in
Phys. Rev.
Geodesic Congruences in the Palatini f(R) Theory
We shall investigate the properties of a congruence of geodesics in the
framework of Palatini f(R) theories. We shall evaluate the modified geodesic
deviation equation and the Raychaudhuri's equation and show that f(R) Palatini
theories do not necessarily lead to attractive forces. Also we shall study
energy condition for f(R) Palatini gravity via a perturbative analysis of the
Raychaudhuri's equation
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
On the fate of singularities and horizons in higher derivative gravity
We study static spherically symmetric solutions of high derivative gravity
theories, with 4, 6, 8 and even 10 derivatives. Except for isolated points in
the space of theories with more than 4 derivatives, only solutions that are
nonsingular near the origin are found. But these solutions cannot smooth out
the Schwarzschild singularity without the appearance of a second horizon. This
conundrum, and the possibility of singularities at finite r, leads us to study
numerical solutions of theories truncated at four derivatives. Rather than two
horizons we are led to the suggestion that the original horizon is replaced by
a rapid nonsingular transition from weak to strong gravity. We also consider
this possibility for the de Sitter horizon.Comment: 15 pages, 3 figures, improvements and references added, to appear in
PR
Self force in 2+1 electrodynamics
The radiation reaction problem for an electric charge moving in flat
space-time of three dimensions is discussed. The divergences stemming from the
pointness of the particle are studied. A consistent regularization procedure is
proposed, which exploits the Poincar\'e invariance of the theory. Effective
equation of motion of radiating charge in an external electromagnetic field is
obtained via the consideration of energy-momentum and angular momentum
conservation. This equation includes the effect of the particle's own field.
The radiation reaction is determined by the Lorentz force of point-like charge
acting upon itself plus a non-local term which provides finiteness of the
self-action.Comment: 20 pages, 3 figure
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