# Quasinormal modes as a distinguisher between general relativity and f(R) gravity

## TL;DR

This paper investigates how quasinormal modes differ between general relativity and f(R) gravity, demonstrating that the relation between scalar and vector perturbations breaks down in f(R) models, which could help test deviations from GR.

## Contribution

It explicitly shows that the relation between scalar and vector perturbations in black holes does not hold in f(R) gravity, providing a potential observational test to distinguish it from GR.

## Key findings

- The relation between Regge-Wheeler and Zerilli perturbations breaks down in f(R) gravity.
- The imbalance in gravitational energy emission can serve as a probe for deviations from GR.
- Implications for observations and the no-hair conjecture are discussed.

## Abstract

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 Regge-Wheeler 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.