1,896 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
Gravitational waves from binary systems in circular orbits: Convergence of a dressed multipole truncation
The gravitational radiation originating from a compact binary system in
circular orbit is usually expressed as an infinite sum over radiative multipole
moments. In a slow-motion approximation, each multipole moment is then
expressed as a post-Newtonian expansion in powers of v/c, the ratio of the
orbital velocity to the speed of light. The bare multipole truncation of the
radiation consists in keeping only the leading-order term in the post-Newtonian
expansion of each moment, but summing over all the multipole moments. In the
case of binary systems with small mass ratios, the bare multipole series was
shown in a previous paper to converge for all values v/c < 2/e, where e is the
base of natural logarithms. In this paper, we extend the analysis to a dressed
multipole truncation of the radiation, in which the leading-order moments are
corrected with terms of relative order (v/c)^2 and (v/c)^3. We find that the
dressed multipole series converges also for all values v/c < 2/e, and that it
coincides (within 1%) with the numerically ``exact'' results for v/c < 0.2.Comment: 9 pages, ReVTeX, 1 postscript figur
Intrinsic and extrinsic geometries of a tidally deformed black hole
A description of the event horizon of a perturbed Schwarzschild black hole is
provided in terms of the intrinsic and extrinsic geometries of the null
hypersurface. This description relies on a Gauss-Codazzi theory of null
hypersurfaces embedded in spacetime, which extends the standard theory of
spacelike and timelike hypersurfaces involving the first and second fundamental
forms. We show that the intrinsic geometry of the event horizon is invariant
under a reparameterization of the null generators, and that the extrinsic
geometry depends on the parameterization. Stated differently, we show that
while the extrinsic geometry depends on the choice of gauge, the intrinsic
geometry is gauge invariant. We apply the formalism to solutions to the vacuum
field equations that describe a tidally deformed black hole. In a first
instance we consider a slowly-varying, quadrupolar tidal field imposed on the
black hole, and in a second instance we examine the tide raised during a close
parabolic encounter between the black hole and a small orbiting body.Comment: 27 pages, 4 figure
Spatial Disorientation: Past, Present, and Future
A proposed Attitude Stabilization Display (ASD) is evaluated against the traditional Attitude Indicator (AI). To understand the merit of this research, U.S. Air Force Class A spatial disorientation (SD) mishaps over the past 21 years were analyzed. This analysis applied Human Factors Analysis and Classification System codes to determine mishaps involving SD. This data was combined with data from the Reliability and Maintainability Information System to determine accident rates per flight hour. Seventy-two SD mishaps were analyzed, resulting in the loss of 101 lives and 65 aircraft since fiscal year (FY) 1993 for a total cost of $2.32 billion. Results indicate that future SD research should be focused on fighter/attack and helicopter platforms. With these results as the motivation, the graphical portions of the ASD were compared to the AI through a desktop flight simulation experiment in which participants used each display to recover from unusual attitudes. Participants completed recovery tasks approximately 2 seconds faster with the AI, on average. This time difference was greatest for participants having flight experience. Survey responses revealed that certain ASD design choices could be beneficial. Further investigation of the ASD is recommended as are updates to the Air Force safety center database
Transition from adiabatic inspiral to plunge into a spinning black hole
A test particle of mass mu on a bound geodesic of a Kerr black hole of mass M
>> mu will slowly inspiral as gravitational radiation extracts energy and
angular momentum from its orbit. This inspiral can be considered adiabatic when
the orbital period is much shorter than the timescale on which energy is
radiated, and quasi-circular when the radial velocity is much less than the
azimuthal velocity. Although the inspiral always remains adiabatic provided mu
<< M, the quasi-circular approximation breaks down as the particle approaches
the innermost stable circular orbit (ISCO). In this paper, we relax the
quasi-circular approximation and solve the radial equation of motion explicitly
near the ISCO. We use the requirement that the test particle's 4-velocity
remain properly normalized to calculate a new contribution to the difference
between its energy and angular momentum. This difference determines how a black
hole's spin changes following a test-particle merger, and can be extrapolated
to help predict the mass and spin of the final black hole produced in
finite-mass-ratio black-hole mergers. Our new contribution is particularly
important for nearly maximally spinning black holes, as it can affect whether a
merger produces a naked singularity.Comment: 9 pages, 6 figures, final version published in PRD with minor change
An improved effective-one-body Hamiltonian for spinning black-hole binaries
Building on a recent paper in which we computed the canonical Hamiltonian of
a spinning test particle in curved spacetime, at linear order in the particle's
spin, we work out an improved effective-one-body (EOB) Hamiltonian for spinning
black-hole binaries. As in previous descriptions, we endow the effective
particle not only with a mass m, but also with a spin S*. Thus, the effective
particle interacts with the effective Kerr background (having spin S_Kerr)
through a geodesic-type interaction and an additional spin-dependent
interaction proportional to S*. When expanded in post-Newtonian (PN) orders,
the EOB Hamiltonian reproduces the leading order spin-spin coupling and the
spin-orbit coupling through 2.5PN order, for any mass-ratio. Also, it
reproduces all spin-orbit couplings in the test-particle limit. Similarly to
the test-particle limit case, when we restrict the EOB dynamics to spins
aligned or antialigned with the orbital angular momentum, for which circular
orbits exist, the EOB dynamics has several interesting features, such as the
existence of an innermost stable circular orbit, a photon circular orbit, and a
maximum in the orbital frequency during the plunge subsequent to the inspiral.
These properties are crucial for reproducing the dynamics and
gravitational-wave emission of spinning black-hole binaries, as calculated in
numerical relativity simulations.Comment: 22 pages, 9 figures. Minor changes to match version accepted for
publication in PR
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
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