Quasinormal modes for arbitrary spins in the Schwarzschild background

TL;DR

This paper analytically derives the asymptotic quasinormal mode frequencies for arbitrary spins in the Schwarzschild background, revealing that the first correction term vanishes for odd integer spins and providing a general correction formula.

Contribution

It provides the first analytical derivation of the first correction to the asymptotic quasinormal mode frequencies for all spins in Schwarzschild spacetime.

Findings

Leading term of quasinormal modes is -i n/2.

First correction vanishes for odd integer spins.

General correction formula derived for all spins.

Abstract

The leading term of the asymptotic of quasinormal modes in the Schwarzschild background, omega_n = - i n/2, is obtained in two straightforward analytical ways for arbitrary spins. One of these approaches requires almost no calculations. As simply we demonstrate that for any odd integer spin, described by the Teukolsky equation, the first correction to the leading term vanishes. Then, this correction for half-integer spins is obtained in a slightly more intricate way. At last, we derive analytically the general expression for the first correction for all spins, described by the Teukolsky equation.