Second-order perturbation theory: Problems on large scales

Adam Pound
Phys. Rev. D 92, 104047 – Published 24 November 2015

Abstract

In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well known that self-force effects accumulate over time, making the geodesic approximation fail on long time scales. It is less well known that this failure at large times translates to a failure at large distances as well. At second perturbative order, two large-distance pathologies arise: spurious secular growth and infrared-divergent retarded integrals. Both stand in the way of practical computations of second-order self-force effects. Utilizing a simple flat-space scalar toy model, I develop methods to overcome these obstacles. The secular growth is tamed with a multiscale expansion that captures the system’s slow evolution. The divergent integrals are eliminated by matching to the correct retarded solution at large distances. I also show how to extract conservative self-force effects by taking local-in-time “snapshots” of the global solution. These methods are readily adaptable to the physically relevant case of a point mass orbiting a black hole.

  • Received 17 October 2015

DOI:https://doi.org/10.1103/PhysRevD.92.104047

© 2015 American Physical Society

Authors & Affiliations

Adam Pound

  • Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom

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Issue

Vol. 92, Iss. 10 — 15 November 2015

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