6,112 research outputs found
Origin of black string instability
It is argued that many nonextremal black branes exhibit a classical
Gregory-Laflamme (GL) instability. Why does the universal instability exist? To
find an answer to this question and explore other possible instabilities, we
study stability of black strings for all possible types of gravitational
perturbation. The perturbations are classified into tensor-, vector-, and
scalar-types, according to their behavior on the spherical section of the
background metric. The vector and scalar perturbations have exceptional
multipole moments, and we have paid particular attention to them. It is shown
that for each type of perturbations there is no normalizable negative
(unstable) modes, apart from the exceptional mode known as s-wave perturbation
which is exactly the GL mode. We discuss the origin of instability and comment
on the implication for the correlated-stability conjecture.Comment: 19 pages (revtex4), 4 figures; references added, minor correction
Second Order Gravitational Self-Force
The second-order gravitational self-force on a small body is an important
problem for gravitational-wave astronomy of extreme mass-ratio inspirals. We
give a first-principles derivation of a prescription for computing the first
and second perturbed metric and motion of a small body moving through a vacuum
background spacetime. The procedure involves solving for a "regular field" with
a specified (sufficiently smooth) "effective source", and may be applied in any
gauge that produces a sufficiently smooth regular field
Gauge and Averaging in Gravitational Self-force
A difficulty with previous treatments of the gravitational self-force is that
an explicit formula for the force is available only in a particular gauge
(Lorenz gauge), where the force in other gauges must be found through a
transformation law once the Lorenz gauge force is known. For a class of gauges
satisfying a ``parity condition'' ensuring that the Hamiltonian center of mass
of the particle is well-defined, I show that the gravitational self-force is
always given by the angle-average of the bare gravitational force. To derive
this result I replace the computational strategy of previous work with a new
approach, wherein the form of the force is first fixed up to a gauge-invariant
piece by simple manipulations, and then that piece is determined by working in
a gauge designed specifically to simplify the computation. This offers
significant computational savings over the Lorenz gauge, since the Hadamard
expansion is avoided entirely and the metric perturbation takes a very simple
form. I also show that the rest mass of the particle does not evolve due to
first-order self-force effects. Finally, I consider the ``mode sum
regularization'' scheme for computing the self-force in black hole background
spacetimes, and use the angle-average form of the force to show that the same
mode-by-mode subtraction may be performed in all parity-regular gauges. It
appears plausible that suitably modified versions of the Regge-Wheeler and
radiation gauges (convenient to Schwarzschild and Kerr, respectively) are in
this class
A Rigorous Derivation of Electromagnetic Self-force
During the past century, there has been considerable discussion and analysis
of the motion of a point charge, taking into account "self-force" effects due
to the particle's own electromagnetic field. We analyze the issue of "particle
motion" in classical electromagnetism in a rigorous and systematic way by
considering a one-parameter family of solutions to the coupled Maxwell and
matter equations corresponding to having a body whose charge-current density
and stress-energy tensor scale to zero size
in an asymptotically self-similar manner about a worldline as . In this limit, the charge, , and total mass, , of the body go to
zero, and goes to a well defined limit. The Maxwell field
is assumed to be the retarded solution associated with
plus a homogeneous solution (the "external field") that varies
smoothly with . We prove that the worldline must be a
solution to the Lorentz force equations of motion in the external field
. We then obtain self-force, dipole forces, and spin force
as first order perturbative corrections to the center of mass motion of the
body. We believe that this is the first rigorous derivation of the complete
first order correction to Lorentz force motion. We also address the issue of
obtaining a self-consistent perturbative equation of motion associated with our
perturbative result, and argue that the self-force equations of motion that
have previously been written down in conjunction with the "reduction of order"
procedure should provide accurate equations of motion for a sufficiently small
charged body with negligible dipole moments and spin. There is no corresponding
justification for the non-reduced-order equations.Comment: 52 pages, minor correction
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
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