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The geometry around a rotating massive body, which carries charge andelectrical currents, could be described by its multipole moments (mass moments,mass-current moments, electric moments, and magnetic moments). When a smallbody is orbiting this massive body, it will move on geodesics, at least for atime interval that is short with respect to the characteristic time of thebinary due to gravitational radiation. By monitoring the waves emitted by thesmall body we are actually tracing the geometry of the central object, andhence, in principle, we can infer all its multipole moments. This paper is ageneralization of previous similar results by Ryan. The fact that theelectromagnetic moments of spacetime can be measured demonstrates that one canobtain information about the electromagnetic field purely from gravitationalwave analysis. Additionally, these measurements could be used as a test of theno-hair theorem for black holes.Comment: Submitted to Phys. Rev.

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