Quasi-local contribution to the scalar self-force: Geodesic Motion

TL;DR

This paper calculates the quasi-local scalar self-force on a particle in curved spacetime, simplifying the expression under certain conditions and exploring implications for gravitational wave sources like binary black holes.

Contribution

It provides a general formula for the quasi-local scalar self-force on a geodesic particle in curved spacetime, with simplifications for massless fields in vacuum backgrounds.

Findings

Derived a simplified expression for the self-force in specific cases.

Applied the results to systems relevant for LISA gravitational wave detection.

Validated the approach using alternative techniques.

Abstract

We consider a scalar charge travelling in a curved background spacetime. We calculate the quasi-local contribution to the scalar self-force experienced by such a particle following a geodesic in a general spacetime. We also show that if we assume a massless field and a vacuum background spacetime, the expression for the self-force simplifies significantly. We consider some specific cases whose gravitational analog are of immediate physical interest for the calculation of radiation reaction corrected orbits of binary black hole systems. These systems are expected to be detectable by the LISA space based gravitational wave observatory. We also investigate how alternate techniques may be employed in some specific cases and use these as a check on our own results.