Overtones of black holes via time-domain integration

TL;DR

This paper demonstrates that the time-domain integration method can effectively compute multiple overtones of quasinormal modes for asymptotically de Sitter black holes, unlike in flat cases where only the fundamental mode is reliably extracted.

Contribution

It introduces a method to calculate overtones of black hole quasinormal modes in de Sitter spacetimes using time-domain integration, highlighting its advantage over traditional methods.

Findings

Overtones can be calculated at low multipole numbers for de Sitter black holes.

Time-domain integration outperforms Prony method in de Sitter cases.

Absence of power-law tails enhances mode extraction accuracy.

Abstract

We show that first several overtones could calculated by the time-domain integration method for asymptotically de Sitter black holes already at the lowest multipole numbers of gravitational and electromagnetic perturbations. This is not possible for asymptotically flat black holes, for which extraction of frequencies with the Prony method is usually possible with reasonable accuracy only for the fundamental mode. The reason for much better efficiency in the de Sitter case is absence of power-law tails: the quasinormal modes dominate the signal not only at the intermediate stage, but also at asymptotically late times.