Nonlinear gravitational self-force: second-order equation of motion
Nonlinear gravitational self-force: second-order equation of motion
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.
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
31 May 2017
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Pound, Adam
(2017)
Nonlinear gravitational self-force: second-order equation of motion.
Physical Review D, 95 (10), [104056].
(doi:10.1103/PhysRevD.95.104056).
Abstract
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.
Text
second-order-partII
- Accepted Manuscript
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Submitted date: 8 March 2017
Accepted/In Press date: 9 May 2017
e-pub ahead of print date: 31 May 2017
Published date: 31 May 2017
Organisations:
Applied Mathematics
Identifiers
Local EPrints ID: 411013
URI: http://eprints.soton.ac.uk/id/eprint/411013
ISSN: 1550-7998
PURE UUID: 7d8137bf-b596-44e7-b72f-f9d384f1f845
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Date deposited: 13 Jun 2017 16:31
Last modified: 16 Mar 2024 04:09
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