17 research outputs found
Gauge Problem in the Gravitational Self-Force II. First Post Newtonian Force under Regge-Wheeler Gauge
We discuss the gravitational self-force on a particle in a black hole
space-time. For a point particle, the full (bare) self-force diverges. It is
known that the metric perturbation induced by a particle can be divided into
two parts, the direct part (or the S part) and the tail part (or the R part),
in the harmonic gauge, and the regularized self-force is derived from the R
part which is regular and satisfies the source-free perturbed Einstein
equations. In this paper, we consider a gauge transformation from the harmonic
gauge to the Regge-Wheeler gauge in which the full metric perturbation can be
calculated, and present a method to derive the regularized self-force for a
particle in circular orbit around a Schwarzschild black hole in the
Regge-Wheeler gauge. As a first application of this method, we then calculate
the self-force to first post-Newtonian order. We find the correction to the
total mass of the system due to the presence of the particle is correctly
reproduced in the force at the Newtonian order.Comment: Revtex4, 43 pages, no figure. Version to be published in PR
Self-gravitating ring of matter in orbit around a black hole: the innermost stable circular orbit
Self-force: Computational Strategies
Building on substantial foundational progress in understanding the effect of
a small body's self-field on its own motion, the past 15 years has seen the
emergence of several strategies for explicitly computing self-field corrections
to the equations of motion of a small, point-like charge. These approaches
broadly fall into three categories: (i) mode-sum regularization, (ii) effective
source approaches and (iii) worldline convolution methods. This paper reviews
the various approaches and gives details of how each one is implemented in
practice, highlighting some of the key features in each case.Comment: Synchronized with final published version. Review to appear in
"Equations of Motion in Relativistic Gravity", published as part of the
Springer "Fundamental Theories of Physics" series. D. Puetzfeld et al.
(eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of
Physics 179, Springer, 201
A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems
Extreme mass ratio binary systems, binaries involving stellar mass objects
orbiting massive black holes, are considered to be a primary source of
gravitational radiation to be detected by the space-based interferometer LISA.
The numerical modelling of these binary systems is extremely challenging
because the scales involved expand over several orders of magnitude. One needs
to handle large wavelength scales comparable to the size of the massive black
hole and, at the same time, to resolve the scales in the vicinity of the small
companion where radiation reaction effects play a crucial role. Adaptive finite
element methods, in which quantitative control of errors is achieved
automatically by finite element mesh adaptivity based on posteriori error
estimation, are a natural choice that has great potential for achieving the
high level of adaptivity required in these simulations. To demonstrate this, we
present the results of simulations of a toy model, consisting of a point-like
source orbiting a black hole under the action of a scalar gravitational field.Comment: 29 pages, 37 figures. RevTeX 4.0. Minor changes to match the
published versio
Analytic approximations, perturbation methods, and their applications
The paper summarizes the parallel session B3 {\em Analytic approximations,
perturbation methods, and their applications} of the GR18 conference. The talks
in the session reported notably recent advances in black hole perturbations and
post-Newtonian approximations as applied to sources of gravitational waves.Comment: Summary of the B3 parallel session of the GR18 conferenc
The Carter Constant for Inclined Orbits About a Massive Kerr Black Hole: near-circular, near-polar orbits
In an extreme mass-ratio binary black hole system, a non-equatorial orbit
will list (i.e. increase its angle of inclination, {\iota}) as it evolves in
Kerr spacetime. The abutment, a set of evolving, near-polar, retrograde orbits,
for which the instantaneous Carter constant (Q) is at its maximum value (Q_{X})
for given values of latus rectum (l) and eccentricity (e), has been introduced
as a laboratory in which the consistency of dQ/dt with corresponding evolution
equations for dl/dt and de/dt might be tested independently of a specific
radiation back-reaction model. To demonstrate the use of the abutment as such a
laboratory, a derivation of dQ/dt, based only on published formulae for dl/dt
and de/dt, was performed for elliptical orbits on the abutment. The resulting
expression for dQ/dt matched the published result to the second order in e. We
believe the abutment is a potentially useful tool for improving the accuracy of
evolution equations to higher orders of e and l^{1}.Comment: 35 Pages, 1 figure, Accepted for publication in Cent Eur J Phy
Intermediate and extreme mass-ratio inspirals — astrophysics, science applications and detection using LISA
Black hole binaries with extreme (gtrsim104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany