Self-force on a static particle near a black hole

Pavel Krtouš and Andrei Zelnikov
Phys. Rev. D 102, 024065 – Published 22 July 2020

Abstract

We study the self-force acting on a static charged pointlike particle near a Schwarzschild black hole. We obtain the pointlike particle as a limit of a spacetime describing a big neutral black hole with a small charged massive object nearby. The massive object is modeled by a black hole or a naked singularity. In this fully interacting system the massive object is supported above the black hole by a strut. Such a strut has a nonzero tension which corresponds to the external force compensating the gravitational force and the electromagnetic self-force acting on the massive object. We discuss details of the limiting procedure leading to the pointlike particle situation. As a result, we obtain the standard gravitational force in the static frame of the Schwarzschild spacetime and the electromagnetic self-force. The electromagnetic self-force differs slightly from the classical results in a domain near the horizon. The difference is due to taking into account the influence of the strut on the electromagnetic field. We also demonstrate that higher order corrections to the gravitational force, a sort of gravitational self-force, are not uniquely defined, and they depend on details of the limiting procedure.

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  • Received 17 October 2019
  • Accepted 2 July 2020

DOI:https://doi.org/10.1103/PhysRevD.102.024065

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Pavel Krtouš1,* and Andrei Zelnikov2,†

  • 1Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, Prague 180 00, Czech Republic
  • 2Theoretical Physics Institute, Department of Physics University of Alberta, Edmonton, Alberta T6G 2E1, Canada

  • *Pavel.Krtous@utf.mff.cuni.cz
  • zelnikov@ualberta.ca

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Vol. 102, Iss. 2 — 15 July 2020

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