# Analytical quasinormal modes of spherically symmetric black holes in the eikonal regime

## TL;DR

This paper derives analytical expressions for high-frequency quasinormal modes of spherically symmetric black holes, including deviations from Einstein's gravity, highlighting their relation to null geodesics and potential instabilities.

## Contribution

It provides a generic formula for eikonal quasinormal modes in asymptotically flat spacetimes with deviations from Schwarzschild geometry.

## Key findings

- Analytical quasinormal modes for various gravity theories.
- Corrections to Schwarzschild eikonal modes due to deviations.
- A generic formula for modes in asymptotically flat metrics.

## Abstract

Quasinormal modes in the high frequency (eikonal) regime can be obtained analytically as the Mashhoon-Will-Schiutz WKB formula is exact in this case. This regime is interesting because of the correspondence between eikonal quasinormal modes and null geodesics, as well as due to existence of potential eikonal instabilities in some theories of gravity. At the same time in a number of studies devoted to quasinormal modes of spherically symmetric black holes this opportunity was omitted. Here we find analytical quasinormal modes of black holes in various alternative and extended theories of gravity in the form of the Schwarzschld eikonal quasinormal modes and added corrections due to deviations from Einstein theory. We also deduce a generic formula for analytical calculations of the eikonal quasinormal modes for the class of asymptotically flat metrics in terms of small deviations from the Schwarzschild geometry.