Gravitational self-force and conservative effects: a testing ground for theories of gravity

TL;DR

This paper investigates how conservative effects in gravitational self-force can serve as a testing ground for different theories of gravity, especially in the context of extreme-mass-ratio inspirals and the upcoming LISA mission.

Contribution

It introduces a method to compare theories of gravity using self-force corrections to gauge-invariant benchmarks and explores the impact of variable gravitational constant G in extended theories.

Findings

Conservative effects can distinguish between General Relativity and alternative theories.

Self-force corrections influence orbital frequency and spin-precession in strong gravitational fields.

The approach provides a framework for testing gravity theories with upcoming gravitational wave observations.

Abstract

Considering extreme-mass-ratio inspirals along with the conservative dynamics of gravitational self-force, we compare viable theories of gravity. In particular, by examining a Schwarzschild background we analyse the self-force-induced corrections to gauge-invariant benchmarks given by the orbital frequency at the ISCO and the spin-precession rate. Moreover, following an established indication of modifications to the equations of motion in extended theories of gravity, we exploit a phenomenological approach, relying on the variability of the gravitational constant G, to incorporate these modifications. We find that conservative effects shape up to be a test-bed for theories of gravity, allowing us to contrast General Relativity with competing theories. By examining strong-field constraints, we highlight a wide margin of investigation in the context of LISA Mission.