187 research outputs found

### Gauge and motion in perturbation theory

Through second order in perturbative general relativity, a small compact
object in an external vacuum spacetime obeys a generalized equivalence
principle: although it is accelerated with respect to the external background
geometry, it is in free fall with respect to a certain \emph{effective} vacuum
geometry. However, this single principle takes very different mathematical
forms, with very different behaviors, depending on how one treats perturbed
motion. Furthermore, any description of perturbed motion can be altered by a
gauge transformation. In this paper, I clarify the relationship between two
treatments of perturbed motion and the gauge freedom in each. I first show
explicitly how one common treatment, called the Gralla-Wald approximation, can
be derived from a second, called the self-consistent approximation. I next
present a general treatment of smooth gauge transformations in both
approximations, in which I emphasise that the approximations' governing
equations can be formulated in an invariant manner. All of these analyses are
carried through second perturbative order, but the methods are general enough
to go to any order. Furthermore, the tools I develop, and many of the results,
should have broad applicability to any description of perturbed motion,
including osculating-geodesic and two-timescale descriptions.Comment: 26 pages, 3 figures. Minor corrections. Equations (120) and (126) are
more general than in PRD versio

### A practical, covariant puncture for second-order self-force calculations

Accurately modeling an extreme-mass-ratio inspiral requires knowledge of the
second-order gravitational self-force on the inspiraling small object.
Recently, numerical puncture schemes have been formulated to calculate this
force, and their essential analytical ingredients have been derived from first
principles. However, the \emph{puncture}, a local representation of the small
object's self-field, in each of these schemes has been presented only in a
local coordinate system centered on the small object, while a numerical
implementation will require the puncture in coordinates covering the entire
numerical domain. In this paper we provide an explicit covariant self-field as
a local expansion in terms of Synge's world function. The self-field is written
in the Lorenz gauge, in an arbitrary vacuum background, and in forms suitable
for both self-consistent and Gralla-Wald-type representations of the object's
trajectory. We illustrate the local expansion's utility by sketching the
procedure of constructing from it a numerically practical puncture in any
chosen coordinate system.Comment: 23 pages, 1 figure, final version to be published in Phys Rev

### Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order

Using black hole perturbation theory and arbitrary-precision computer
algebra, we obtain the post-Newtonian (pN) expansions of the
linear-in-mass-ratio corrections to the spin-precession angle and tidal
invariants for a particle in circular orbit around a Schwarzschild black hole.
We extract coefficients up to 20pN order from numerical results that are
calculated with an accuracy greater than 1 part in $10^{500}$. These results
can be used to calibrate parameters in effective-one-body models of compact
binaries, specifically the spin-orbit part of the effective Hamiltonian and the
dynamically significant tidal part of the main radial potential of the
effective metric. Our calculations are performed in a radiation gauge, which is
known to be singular away from the particle. To overcome this irregularity, we
define suitable Detweiler-Whiting singular and regular fields in this gauge,
and we devise a rigorous mode-sum regularization method to compute the
invariants constructed from the regular field

### Commission des Communautes Europeennes: Groupe du Porte-Parole. Rendez-vous de midi du 11 fevrier 1981 (J. Carroll) = Commission of European Communities: Spokesman Group. Appointment on the afternoon of 11 February 1981 (J. Carroll). Spokesman Service Note to National Offices Bio No. (81) 50, 13 February 1981

When a small, uncharged, compact object is immersed in an external background spacetime, at zeroth order in its mass it moves as a test particle in the background. At linear order, its own gravitational field alters the geometry around it, and it moves instead as a test particle in a certain effective metric satisfying the linearized vacuum Einstein equation. In the letter [Phys. Rev. Lett. 109, 051101 (2012)], using a method of matched asymptotic expansions, I showed that the same statement holds true at second order: if the object's leading-order spin and quadrupole moment vanish, then through second order in its mass it moves on a geodesic of a certain smooth, locally causal vacuum metric defined in its local neighbourhood. Here I present the complete details of the derivation of that result. In addition, I extend the result, which had previously been derived in gauges smoothly related to Lorenz, to a class of highly regular gauges that should be optimal for numerical self-force computations

### Gravitational self-force from radiation-gauge metric perturbations

Calculations of the gravitational self-force (GSF) on a point mass in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the metric perturbation is formulated in a class of â€śradiationâ€ť gauges, in which the particle singularity is nonisotropic and extends away from the particleâ€™s location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We show that three types of radiation gauge exist: two containing a radial stringlike singularity emanating from the particle, either in one direction (â€śhalf-stringâ€ť gauges) or both directions (â€śfull-stringâ€ť gauges); and a third type containing no strings but with a jump discontinuity (and possibly a delta function) across a surface intersecting the particle. Based on a flat-space example, we argue that the standard mode-by-mode reconstruction procedure yields the â€śregular halfâ€ť of a half-string solution, or (equivalently) either of the regular halves of a no-string solution. For the half-string case, we formulate the GSF in a locally deformed radiation gauge that removes the string singularity near the particle. We derive a mode-sum formula for the GSF in this gauge, which is analogous to the standard Lorenz-gauge formula but requires a correction to the values of the regularization parameters. For the no-string case, we formulate the GSF directly, without a local deformation, and we derive a mode-sum formula that requires no correction to the regularization parameters but involves a certain averaging procedure. We explain the consistency of our results with Grallaâ€™s invariance theorem for the regularization parameters, and we discuss the correspondence between our method and a related approach by Friedman et al

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