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

TL;DR

This paper investigates how quasinormal modes can distinguish between general relativity and f(R) gravity by analyzing charged black holes and their perturbation energetics.

Contribution

It introduces a method to estimate black hole charge from QNM energetics in GR and extends this analysis to f(R) theories to identify deviations.

Findings

A dimensionless parameter estimates black hole charge in GR.

Modified theories show distinct energy radiations in scalar and vector modes.

Method provides a way to quantify deviations from general relativity.

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. In General relativity, we identify a dimensionless parameter that can estimate the charge of a black-hole from the energetics of quasi-normal modes. We then extend the analysis for f(R) theories of gravity. Using Isaacson's prescription to modified theories of gravity, we obtain an accurate and robust method to estimate the difference in the radiated energies in the scalar and vector modes due to modifications to general relativity. We then discuss how to quantify the deviation from general relativity.