Method of Matched Expansions & the Singularity Structure of the Green Function

TL;DR

This paper demonstrates the first successful use of the method of Matched Expansions to compute the self-force on a scalar charge in curved spacetime, analyzing Green function singularities and caustic effects.

Contribution

It introduces the application of the method of Matched Expansions to self-force calculations in curved spacetime, focusing on the Nariai spacetime as a model.

Findings

Green function singularity structure beyond normal neighbourhood

Effect of caustics on null wave propagation

Validation of method in a toy model for black hole background

Abstract

We present the first successful application of the method of Matched Expansions for the calculation of the self-force on a point particle in a curved spacetime. We investigate the case of a scalar charge in the Nariai spacetime, which serves as a toy model for a point mass moving in the Schwarzschild black hole background. We discuss the singularity structure of the Green function beyond the normal neighbourhood and the interesting effect of caustics on null wave propagation.