# Two approaches for the gravitational self force in black hole spacetime: comparison of numerical results

Sago, Norichika, Barack, Leor and Detweiler, Steven
(2008)
Two approaches for the gravitational self force in black hole spacetime: comparison of numerical results.
*Physical Review D*, 78, (12), 124024-[9pp]. (doi:10.1103/PhysRevD.78.124024).

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## Description/Abstract

Recently, two independent calculations have been presented of finite-mass (“self-force”) effects on the orbit of a point mass around a Schwarzschild black hole. While both computations are based on the standard mode-sum method, they differ in several technical aspects, which makes comparison between their results difficult—but also interesting. Barack and Sago [Phys. Rev. D 75, 064021 (2007)] invoke the notion of a self-accelerated motion in a background spacetime, and perform a direct calculation of the local self-force in the Lorenz gauge (using numerical evolution of the perturbation equations in the time domain); Detweiler [Phys. Rev. D 77, 124026 (2008)] describes the motion in terms a geodesic orbit of a (smooth) perturbed spacetime, and calculates the metric perturbation in the Regge-Wheeler gauge (using frequency-domain numerical analysis). Here we establish a formal correspondence between the two analyses, and demonstrate the consistency of their numerical results. Specifically, we compare the value of the conservative O(μ) shift in ut (where μ is the particle’s mass and ut is the Schwarzschild t component of the particle’s four-velocity), suitably mapped between the two orbital descriptions and adjusted for gauge. We find that the two analyses yield the same value for this shift within mere fractional differences of ∼10-5–10-7 (depending on the orbital radius)—comparable with the estimated numerical error.

Item Type: | Article |
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ISSNs: | 1550-7998 (print) 1089-4918 (electronic) |

Subjects: | Q Science > QA Mathematics Q Science > QC Physics |

Divisions: | University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics |

ePrint ID: | 63997 |

Date Deposited: | 24 Nov 2008 |

Last Modified: | 27 Mar 2014 18:45 |

URI: | http://eprints.soton.ac.uk/id/eprint/63997 |

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