2008/10/31 by Norichika Sago, Leor Barack, Steven Detweiler · 3 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Experimental and Theoretical Physics Studies #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1103/physrevd.78.124024
published as Phys.Rev.D78:124024,2008 · 11 pages; minor typos corrected; final version to be published in PRD
arxiv created 2008/12/10 · openalex publication_date 2008/12/30 · arxiv updated 2010/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(\ensuremathμ) shift in ut (where \ensuremathμ 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 \ensuremath∼10^\ensuremath-5--10^\ensuremath-7 (depending on the orbital radius)---comparable with the estimated numerical error.