Scalar self-force on a static particle in Schwarzschild spacetime using the massive field approach

Abstract

We use the recently developed massive field approach to calculate the scalar self-force on a static particle in a Schwarzschild spacetime. In this approach the scalar self-force is obtained from the difference between the (massless) scalar field, and an auxiliary massive scalar field combined with a certain limiting process. By applying this approach to a static particle in Schwarzschild we show that the scalar self-force vanishes in this case. This result conforms with a previous analysis by Wiseman [9].

Static Kerr Green’s function in closed form and an analytic derivation of the self-force for a static scalar charge in Kerr space-time

“…It is easy to check that Eq. (4.41)-(4.42) gives us zero self-force for a static particle in Schwarzschild, as expected [9,35].…”

Renormalization for the self-potential of a scalar charge in static space-times

“…Note the derivative of (38) ∂φ(r; r 0 )/∂r differs from the corresponding expression in [14] by the term −qM/(6r 0 3 1 − 2M/r 0 ).…”

“…Some of them are reviewed in [10,11]. Note also the zeta function method [12] and the "massive field approach" for the calculation of the self-force [13,14]. In the ultrastatic space-times the renormalization of the field of static charge can be realized by the subtraction of the first terms from DeWitt-Schwinger asymptotic expansion of a three-dimensional Euclidean Green's function [15][16][17][18].…”

Self-force: Computational Strategies

“…Finally, it should be pointed out that this review is not an exhaustive exposition of all self-force computation strategies. Many other calculations have not been described, including alternative regularization strategies [66,181,182], near-horizon waveform calculations [183][184][185][186], methods based on effective field theory [187][188][189][190], analytic calculations in particularly simple cases [95,191,192], black holes in higher dimensions [193], and calculations in non-black hole spacetimes such as wormholes [194,195] and cosmological models [196,197]. More details can be found in the reviews [60,61], and references therein.…”