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.
Highlights
General relativity has been an unprecedented success in describing the majority of astrophysical phenomena
The question that raises is: whether the extra mode leaves any signatures in the quasi-normal mode ringing and provide a new way of distinguishing general relativity from modified theories of gravity? Previous analysis of Reissner–Nördstrom black holes in f (R) theories were done in [28,29,30]
The energetic equality between scalar and vector type gravitational perturbation is broken in the presence of charge in a black-hole
Summary
General relativity has been an unprecedented success in describing the majority of astrophysical phenomena. Its recent successes include the direct detection of gravitational waves from the binary black hole and binary neutron star mergers by the LIGO-VIRGO collaboration [1,2,3] These detections have raised questions about the possibility of obtaining the severe constraints on the degree of validity of general relativity in the strong gravity regimes. Astrophysical black-holes that are in the centers of the galaxies or formed due to the collapse interact with the external surroundings These black-holes are perturbed continuously compared to the exact solutions in general relativity or modified theories of gravity. The question that raises is: whether the extra mode leaves any signatures in the quasi-normal mode ringing and provide a new way of distinguishing general relativity from modified theories of gravity? The various physical quantities with the over-line refer to the values evaluated for the spherically symmetric background, whereas superscript (n) represents the n-th order perturbed quantity
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