Quasi normal modes: A simple derivation of the level spacing of the frequencies

TL;DR

This paper provides a simple derivation showing that the imaginary parts of quasi-normal mode frequencies are equally spaced, a property linked to horizon thermality and exponential redshift, extending previous results beyond Schwarzschild black holes.

Contribution

It generalizes the equal spacing of imaginary parts of quasi-normal modes to a broader class of spacetimes with a straightforward derivation.

Findings

Imaginary parts of frequencies are equally spaced in various spacetimes.

The spacing depends only on surface gravity.

The result is connected to horizon thermality and redshift effects.

Abstract

It is known that the imaginary parts of the frequencies of the quasi normal modes of the Schwarzschild black hole are equally spaced, with the level spacing dependent only on the surface gravity. We generalize this result to a wider class of spacetimes and provide a simple derivation of the imaginary parts of the frequencies. The analysis shows that the result is closely linked to the thermal nature of horizons and arises from the exponential redshift of the wave modes close to the horizon.