Gravitational self-force by mode sum regularization

Leor Barack
Phys. Rev. D 64, 084021 – Published 26 September 2001
PDFExport Citation

Abstract

We propose a practical scheme for calculating the local gravitational self-force experienced by a test mass particle moving in a black hole spacetime. The method—equally effective for either weak or strong field orbits—employs the mode-sum regularization scheme previously developed for a scalar toy model. The starting point for the calculation, in this approach, is the formal expression for the regularized self-force derived by Mino et al. [Phys. Rev. D 55, 3457 (1997)] (and, independently, by Quinn and Wald [Phys. Rev. D 56, 3381 (1997)]), which involves a worldline integral over the tail part of the retarded Green’s function. This force is decomposed into multipole (tensor harmonic) modes, whose sum is subjected to a carefully designed regularization procedure. This procedure involves an analytical derivation of certain “regularization parameters” by means of a local analysis of the Green’s function. This paper contains the following main parts: (1) The introduction of the mode sum scheme as applied to the gravitational case. (2) Two simple cases studied: the test case of a static particle in flat spacetime, and the case of a particle at a turning point of a radial geodesic in Schwarzschild spacetime. In both cases we derive all necessary regularization parameters. (3) An analytical foundation is set for applying the scheme in more general cases. (In this paper, the mode sum scheme is formulated within the harmonic gauge. The implementation of the scheme in other gauges shall be discussed in a separate, forthcoming paper.)

  • Received 11 May 2001

DOI:https://doi.org/10.1103/PhysRevD.64.084021

©2001 American Physical Society

Authors & Affiliations

Leor Barack

  • Department of Physics, Technion—Israel Institute of Technology, Haifa, 32000, Israel
  • Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, D-14476 Golm, Germany

References (Subscription Required)

Click to Expand
Issue

Vol. 64, Iss. 8 — 15 October 2001

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×