# Are eikonal quasinormal modes linked to the unstable circular null geodesics?

## TL;DR

This paper investigates the proposed link between eikonal quasinormal modes and unstable null geodesics in black holes, finding that the connection does not hold universally in Einstein-Lovelock theory but does in other cases.

## Contribution

It provides analytical expressions for gravitational quasinormal modes in Einstein-Lovelock black holes and clarifies the conditions under which the null geodesic–quasinormal mode correspondence holds.

## Key findings

- The link is violated in Einstein-Lovelock black holes.
- The correspondence holds in some other black hole cases.
- Limits of the null geodesic–quasinormal mode relation are formulated.

## Abstract

In Phys. Rev. D 79, 064016 (2009) it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein-Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.