Self-Force on a Scalar Charge in Circular Orbit around a Schwarzschild Black Hole

Details Self-Force on a Scalar Charge in Circular Orbit around a Schwarzschild Black Hole Self-Force on a Scalar Charge in Circular Orbit around a Schwarzschild Black Hole

2001-04-04

arxiv.org/abs/gr-qc/0104012v2

Prog.Theor.Phys.106:339-362,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, no figure, Minor typos corrected

Scientific paper

10.1143/PTP.106.339

In an accompanying paper, we have formulated two types of regulariz_ation methods to calculate the scalar self-force on a particle of charge $q$ moving around a black hole of mass $M$, one of which is called the ``power expansion regularization''. In this paper, we analytically evaluate the self-force (which we also call the reaction force) to the third post-Newtonian (3PN) order on the scalar particle in circular orbit around a Schwarzschild black hole by using the power expansion regularization. It is found that the $r$-component of the self-force arises at the 3PN order, whereas the $t$- and $\phi$-components, which are due to the radiation reaction, appear at the 2PN and 1.5PN orders, respectively.

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