1,813 research outputs found

### Gravitational radiation reaction and second order perturbation theory

A point particle of small mass m moves in free fall through a background
vacuum spacetime metric g_ab and creates a first-order metric perturbation
h^1ret_ab that diverges at the particle. Elementary expressions are known for
the singular m/r part of h^1ret_ab and for its tidal distortion determined by
the Riemann tensor in a neighborhood of m. Subtracting this singular part
h^1S_ab from h^1ret_ab leaves a regular remainder h^1R_ab. The self-force on
the particle from its own gravitational field adjusts the world line at O(m) to
be a geodesic of g_ab+h^1R_ab. The generalization of this description to
second-order perturbations is developed and results in a wave equation
governing the second-order h^2ret_ab with a source that has an O(m^2)
contribution from the stress-energy tensor of m added to a term quadratic in
h^1ret_ab. Second-order self-force analysis is similar to that at first order:
The second-order singular field h^2S_ab subtracted from h^2ret_ab yields the
regular remainder h^2R_ab, and the second-order self-force is then revealed as
geodesic motion of m in the metric g_ab+h^1R+h^2R.Comment: 7 pages, conforms to the version submitted to PR

### A light-cone gauge for black-hole perturbation theory

The geometrical meaning of the Eddington-Finkelstein coordinates of
Schwarzschild spacetime is well understood: (i) the advanced-time coordinate v
is constant on incoming light cones that converge toward r=0, (ii) the angles
theta and phi are constant on the null generators of each light cone, (iii) the
radial coordinate r is an affine-parameter distance along each generator, and
(iv) r is an areal radius, in the sense that 4 pi r^2 is the area of each
two-surface (v,r) = constant. The light-cone gauge of black-hole perturbation
theory, which is formulated in this paper, places conditions on a perturbation
of the Schwarzschild metric that ensure that properties (i)--(iii) of the
coordinates are preserved in the perturbed spacetime. Property (iv) is lost in
general, but it is retained in exceptional situations that are identified in
this paper. Unlike other popular choices of gauge, the light-cone gauge
produces a perturbed metric that is expressed in a meaningful coordinate
system; this is a considerable asset that greatly facilitates the task of
extracting physical consequences. We illustrate the use of the light-cone gauge
by calculating the metric of a black hole immersed in a uniform magnetic field.
We construct a three-parameter family of solutions to the perturbative
Einstein-Maxwell equations and argue that it is applicable to a broader range
of physical situations than the exact, two-parameter Schwarzschild-Melvin
family.Comment: 12 page

### The singular field used to calculate the self-force on non-spinning and spinning particles

The singular field of a point charge has recently been described in terms of
a new Green's function of curved spacetime. This singular field plays an
important role in the calculation of the self-force acting upon the particle.
We provide a method for calculating the singular field and a catalog of
expansions of the singular field associated with the geodesic motion of
monopole and dipole sources for scalar, electromagnetic and gravitational
fields. These results can be used, for example, to calculate the effects of the
self-force acting on a particle as it moves through spacetime.Comment: 14 pages; addressed referee's comments; published in PhysRev

### Gauss-Codazzi thermodynamics on the timelike screen

It is a known result by Jacobson that the flux of energy-matter through a
local Rindler horizon is related with the expansion of the null generators in a
way that mirrors the first law of thermodynamics. We extend such a result to a
timelike screen of observers with finite acceleration. Since timelike curves
have more freedom than null geodesics, the construction is more involved than
Jacobson's and few geometrical constraints need to be imposed: the observers'
acceleration has to be constant in time and everywhere orthogonal to the
screen. Moreover, at any given time, the extrinsic curvature of the screen has
to be flat. The latter requirement can be weakened by asking that the extrinsic
curvature, if present at the beginning, evolves in time like on a cone and just
rescales proportionally to the expansion.Comment: 8+1 pages, final versio

### 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

### 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

### 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

### Horizon-absorption effects in coalescing black-hole binaries: An effective-one-body study of the non-spinning case

We study the horizon absorption of gravitational waves in coalescing,
circularized, nonspinning black hole binaries. The horizon absorbed fluxes of a
binary with a large mass ratio (q=1000) obtained by numerical perturbative
simulations are compared with an analytical, effective-one-body (EOB) resummed
expression recently proposed. The perturbative method employs an analytical,
linear in the mass ratio, effective-one-body (EOB) resummed radiation reaction,
and the Regge-Wheeler-Zerilli (RWZ) formalism for wave extraction.
Hyperboloidal (transmitting) layers are employed for the numerical solution of
the RWZ equations to accurately compute horizon fluxes up to the late plunge
phase. The horizon fluxes from perturbative simulations and the EOB-resummed
expression agree at the level of a few percent down to the late plunge. An
upgrade of the EOB model for nonspinning binaries that includes horizon
absorption of angular momentum as an additional term in the resummed radiation
reaction is then discussed. The effect of this term on the waveform phasing for
binaries with mass ratios spanning 1 to 1000 is investigated. We confirm that
for comparable and intermediate-mass-ratio binaries horizon absorbtion is
practically negligible for detection with advanced LIGO and the Einstein
Telescope (faithfulness greater than or equal to 0.997)

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