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

Norichika Sago, Leor Barack, Steven Detweiler

Research output: Contribution to journalArticlepeer-review

100 Citations (Scopus)


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 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 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.

Original languageEnglish
Article number124024
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number12
Publication statusPublished - Dec 2 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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