Quasinormal modes as a distinguisher between general relativity and f(R) gravity: charged black-holes

Abstract

The ring-down phase of black-hole perturbations is governed by the quasi-normal modes (QNM) and offer valuable insight into the nature of the objects emitting them, raising an interesting question: whether QNMs can be used to distinguish between theories of gravity? We construct a consistency test of general relativity (GR) which enables one to distinguish between general relativity and a specific class of modified theories of gravity: f(R). We show that an energetic inequality between scalar (polar) and vector (axial) type gravitational perturbations will exist for Reissner–Nördstrom solutions of GR - using which we find a novel method of determining the charge of a non-spinning black hole in GR. We then show that there will be a further energetic difference for charged black holes in f(R). Finally, we utilize this extra difference to construct a parameter to quantify deviation from GR.