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

TL;DR

This paper derives a closed-form Green's function for a static scalar charge in Kerr spacetime and uses it to analytically compute the self-force, providing a new exact solution and comparison to existing methods.

Contribution

It presents the first closed-form solution for the Green's function in Kerr spacetime for static scalar charges and derives an analytic expression for the self-force.

Findings

Closed-form Green's function for static scalar charge in Kerr

Analytic expression for the self-force

Comparison with mode-sum regularization results

Abstract

We derive a closed-form solution for the Green's function for the wave equation of a static (with respect to an undragged, static observer at infinity) scalar charge in the Kerr space-time. We employ our solution to obtain an analytic expression for the self-force on such a charge, comparing our results to those previously obtained using the mode-sum regularization prescription.