# Post-Kerr black hole spectroscopy

## TL;DR

This paper develops a formalism for black hole spectroscopy that models deviations from Kerr black holes, enabling tests of gravity through gravitational wave signals by analyzing quasinormal modes.

## Contribution

It introduces a 'post-Kerr' quasinormal mode formalism that incorporates parametrized deviations from Kerr metrics using a perturbative approach and null geodesic properties.

## Key findings

- Derived approximate formulas for quasinormal mode frequencies in the eikonal limit.
- Applied the framework to a deformed Kerr metric to quantify deviations.
- Provided a toolkit for waveform analysis to detect non-Kerr features.

## Abstract

One of the central goals of the newborn field of gravitational wave astronomy is to test gravity in the highly nonlinear, strong field regime characterizing the spacetime of black holes. In particular, "black hole spectroscopy" (the observation and identification of black hole quasinormal mode frequencies in the gravitational wave signal) is expected to become one of the main tools for probing the structure and dynamics of Kerr black holes. In this paper we take a significant step towards that goal by constructing a "post-Kerr" quasinormal mode formalism. The formalism incorporates a parametrized but general perturbative deviation from the Kerr metric and exploits the well-established connection between the properties of the spacetime's circular null geodesics and the fundamental quasinormal mode to provide approximate, eikonal limit formulae for the modes' complex frequencies. The resulting algebraic toolkit can be used in waveform templates for ringing black holes with the purpose of measuring deviations from the Kerr metric. As a first illustrative application of our framework, we consider the Johannsen-Psaltis deformed Kerr metric and compute the resulting deviation in the quasinormal mode frequency relative to the known Kerr result.