Analytic expressions for quasinormal modes of the general parametrized spherically symmetric black holes and the Hod's proposal

TL;DR

This paper derives an analytic expression for quasinormal modes of parametrized spherically symmetric black holes, demonstrating their compliance with Hod's proposal relating damping rates to Hawking temperature.

Contribution

It introduces a new analytic formula for quasinormal modes of general parametrized black holes with small deviations from Schwarzschild geometry.

Findings

Black holes satisfy Hod's proposal linking damping rate and Hawking temperature.

Analytic expressions are valid for small deviations from Schwarzschild.

Method uses inverse multipole expansion and WKB approximation.

Abstract

Using an expansion in terms of the inverse multipole number and the WKB approach, we derive an analytic expression for generic parametrized spherically symmetric and asymptotically flat black holes described by the Rezzolla-Zhidenko spacetime, in the regime when deviations from the Schwarzschild geometry are relatively small, i.e., when the coefficients of the parametrization are small. As an application of this analytic formula, we demonstrate that such generic black holes satisfy Hod's proposal, which constrains the damping rate of the least damped mode in relation to the Hawking temperature.