1,169 research outputs found
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
Are Time-Domain Self-Force Calculations Contaminated by Jost Solutions?
The calculation of the self force in the modeling of the gravitational-wave
emission from extreme-mass-ratio binaries is a challenging task. Here we
address the question of the possible emergence of a persistent spurious
solution in time-domain schemes, referred to as a {\em Jost junk solution} in
the literature, that may contaminate self force calculations. Previous studies
suggested that Jost solutions are due to the use of zero initial data, which is
inconsistent with the singular sources associated with the small object,
described as a point mass. However, in this work we show that the specific
origin is an inconsistency in the translation of the singular sources into jump
conditions. More importantly, we identify the correct implementation of the
sources at late times as the sufficient condition guaranteeing the absence of
Jost junk solutions.Comment: RevTeX. 5 pages, 2 figures. Version updated to match the contents of
the published articl
Solvable and/or integrable and/or linearizable N-body problems in ordinary (three-dimensional) space. I
Several N-body problems in ordinary (3-dimensional) space are introduced
which are characterized by Newtonian equations of motion (``acceleration equal
force;'' in most cases, the forces are velocity-dependent) and are amenable to
exact treatment (``solvable'' and/or ``integrable'' and/or ``linearizable'').
These equations of motion are always rotation-invariant, and sometimes
translation-invariant as well. In many cases they are Hamiltonian, but the
discussion of this aspect is postponed to a subsequent paper. We consider
``few-body problems'' (with, say, \textit{N}=1,2,3,4,6,8,12,16,...) as well as
``many-body problems'' (N an arbitrary positive integer). The main focus of
this paper is on various techniques to uncover such N-body problems. We do not
discuss the detailed behavior of the solutions of all these problems, but we do
identify several models whose motions are completely periodic or multiply
periodic, and we exhibit in rather explicit form the solutions in some cases
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
Le thon : enjeux et stratégies pour l'océan Indien
La pĂȘche rĂ©unionnaise est, depuis les cinq derniĂšres annĂ©es, placĂ©e Ă contre temps complet de l'immense majoritĂ© des autres pĂȘcheries communautaires (Union europĂ©enne), dans une situation de dĂ©veloppement rapide de l'ensemble de ses segments (pĂȘche artisanale, grande pĂȘche hauturiĂšre antarctique, pĂȘche palangriĂšre). Le plus rapide de ces dĂ©veloppements est certainement celui du segment palangrier qui, nĂ© il y a 5 ans, va cette annĂ©e 1996 Ă©galiser, voire dĂ©passer la pĂȘche artisanale, soit prĂšs de 1 500 t/an. Cette pĂȘcherie est composĂ©e par 9 armements alignant 28 navirees de 12 Ă 33 m dont 20 sont opĂ©rationnels en 1996. Sa production est constituĂ©e pour les espĂšces majeures, de 2/3 d'espadons et de 1/3 de thonidĂ©s. La zone de pĂȘche exploitĂ©e est trĂšs vaste, depuis l'Ă©quateur jusqu'au 35°Sud. Les rendements, aprĂšs avoir prĂ©sentĂ© une augmentation trĂšs significative de 1992 Ă 1994, prĂ©sentent un tassement certain de 1994 Ă 1996 pour tous les navires de la flotte. Ce dĂ©veloppement se poursuit aujourd'hui au niveau de la rĂ©gion COI par un dĂ©veloppement des flottilles palangriĂšres rĂ©gionales, amorcĂ© aux Seychelles et bientĂŽt Ă Maurice. Un Ă©quilibre d'exploitation pĂ©renne doit impĂ©rativement s'appuyer sur les recherches halieutiques et socio-Ă©conomiques d'accompagnement de cette pĂȘcherie. (RĂ©sumĂ© d'auteur
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
Relativistic Effects in Extreme Mass Ratio Gravitational Wave Bursts
Extreme mass ratio bursts (EMRBs) have been proposed as a possible source for
future space-borne gravitational wave detectors, such as the Laser
Interferometer Space Antenna (LISA). These events are characterized by
long-period, nearly-radial orbits of compact objects around a central massive
black hole. The gravitational radiation emitted during such events consists of
a short burst, corresponding to periapse passage, followed by a longer, silent
interval. In this paper we investigate the impact of including relativistic
corrections to the description of the compact object's trajectory via a
geodesic treatment, as well as including higher-order multipole corrections in
the waveform calculation. The degree to which the relativistic corrections are
important depends on the EMRB's orbital parameters. We find that relativistic
EMRBs (v_{max}}/c > 0.25) are not rare and actually account for approximately
half of the events in our astrophysical model. The relativistic corrections
tend to significantly change the waveform amplitude and phase relative to a
Newtonian description, although some of this dephasing could be mimicked by
parameter errors. The dephasing over several bursts could be of particular
importance not only to gravitational wave detection, but also to parameter
estimation, since it is highly correlated to the spin of the massive black
hole. Consequently, we postulate that if a relativistic EMRB is detected, such
dephasing might be used to probe the relativistic character of the massive
black hole and obtain information about its spin.Comment: 13 pages, 8 figures, 2 tables. Replaced with version accepted for
publication in the Ap.
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