The University of Southampton
University of Southampton Institutional Repository

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

Record type: Article

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(?) shift in ut (where ? 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.

Full text not available from this repository.


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).

More information

Published date: 30 December 2008
Organisations: Applied Mathematics


Local EPrints ID: 63997
ISSN: 1550-7998
PURE UUID: e178dfc4-857f-4b62-96a3-5d15ca41c501

Catalogue record

Date deposited: 24 Nov 2008
Last modified: 17 Jul 2017 14:14

Export record



Author: Norichika Sago
Author: Leor Barack
Author: Steven Detweiler

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.