Nonlinear gravitational self-force: Field outside a small body

Adam Pound
Phys. Rev. D 86, 084019 – Published 3 October 2012

Abstract

A small extended body moving through an external spacetime gαβ creates a metric perturbation hαβ, which forces the body away from geodesic motion in gαβ. The foundations of this effect, called the gravitational self-force, are now well established, but concrete results have mostly been limited to linear order. Accurately modeling the dynamics of compact binaries requires proceeding to nonlinear orders. To that end, I show how to obtain the metric perturbation outside the body at all orders in a class of generalized wave gauges. In a small buffer region surrounding the body, the form of the perturbation can be found analytically as an expansion for small distances r from a representative worldline. Given only a specification of the body’s multipole moments, the field obtained in the buffer region suffices to find the metric everywhere outside the body via a numerical puncture scheme. Following this procedure at first and second order, I calculate the field in the buffer region around an arbitrarily structured compact body at sufficiently high order in r to numerically implement a second-order puncture scheme, including effects of the body’s spin. I also define nth-order (local) generalizations of the Detweiler-Whiting singular and regular fields and show that in a certain sense, the body can be viewed as a skeleton of multipole moments.

  • Received 27 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.084019

© 2012 American Physical Society

Authors & Affiliations

Adam Pound

  • School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom

See Also

Second-Order Gravitational Self-Force

Adam Pound
Phys. Rev. Lett. 109, 051101 (2012)

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Issue

Vol. 86, Iss. 8 — 15 October 2012

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