Tracing the geometry around a massive, axisymmetric body to measure, through gravitational waves, its mass moments and electromagnetic moments

TL;DR

This paper proposes a method to determine the multipole moments of a rotating, charged massive body using gravitational waves emitted by a small orbiting body, enabling tests of the no-hair theorem and electromagnetic field properties.

Contribution

It generalizes previous work to include electromagnetic moments, allowing extraction of both gravitational and electromagnetic properties from gravitational wave data.

Findings

Electromagnetic moments can be measured from gravitational wave signals.

The method enables testing the no-hair theorem for black holes.

It provides a way to infer the electromagnetic environment of massive bodies.

Abstract

The geometry around a rotating massive body, which carries charge and electrical currents, could be described by its multipole moments (mass moments, mass-current moments, electric moments, and magnetic moments). When a small body is orbiting this massive body, it will move on geodesics, at least for a time interval that is short with respect to the characteristic time of the binary due to gravitational radiation. By monitoring the waves emitted by the small body we are actually tracing the geometry of the central object, and hence, in principle, we can infer all its multipole moments. This paper is a generalization of previous similar results by Ryan. The fact that the electromagnetic moments of spacetime can be measured demonstrates that one can obtain information about the electromagnetic field purely from gravitational wave analysis. Additionally, these measurements could be used as a test of the no-hair theorem for black holes.