Quasi-Normal Modes (QNM) or ringdown phase of gravitational waves provide critical information about the structure of compact objects like Black Holes. Thus, QNMs can be a tool to test General Relativity (GR) and possible deviations from it. In the case of GR, it is known for a long time that a relation between two types of Black Hole perturbations: scalar (Zerilli) and vector (Regge-Wheeler), leads to an equal share of emitted gravitational energy. With the direct detection of Gravitational waves, it is now natural to ask: whether the same relation (between scalar and vector perturbations) holds for modified gravity theories? If not, whether one can use this as a way to probe deviations from General Relativity. As a first step, we show explicitly that the above relation between ReggeWheeler and Zerilli breaks down for a general f (R) model and hence the two perturbations do not share equal amounts of emitted gravitational energy. We discuss the implication of this imbalance on observations and the no-hair conjecture.

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. * xeonese13@iisertvm.ac.in † shanki@phy.iitb.ac.in arXiv:1803.07576v3 [gr-qc] Sep 2018Recently the current authors showed explicitly while the two types of black hole pertur-

Quasi-normal modes (QNMs) uniquely characterize the final black-hole. Till now, only the QNM frequency and damping time are used to test General relativity. In this work, we show explicitly that another property of the QNMstheir polarization -can be a reliable tool for probing gravity. We provide a consistent test for General relativity by considering Chern-Simons gravity. Distinguishing Chern-Simons gravity from General relativity using only template matching is highly challenging. Thus a parameter that can differentiate between Chern-Simons gravity and GR will be a suitable candidate for any modified theories of gravity. We discuss the implications of our result for the future gravitational wave detectors.

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