Time evolution of perturbations in quasi-Schwarzschild black holes

TL;DR

This paper studies how small deviations from General Relativity in black hole perturbation potentials affect the time evolution of signals, revealing richer dynamics and potential new physics beyond frequency domain analysis.

Contribution

It introduces a method to analyze the time evolution of perturbations in quasi-Schwarzschild black holes with potentials slightly deviating from GR, highlighting features not seen in frequency domain.

Findings

Deviations in the potential alter the tail behavior of signals.

New modes or instabilities can emerge due to potential modifications.

Different terms in the potential influence the time profile distinctly.

Abstract

Parametric deviations of quasinormal modes~(QNMs) is a common feature of beyond General Relativity (GR) theories. For theories with additional degrees of freedom, such as scalars and vectors, new family of modes might appear, usually called scalar-led and vector-led modes. Although a power series expansion in terms of the new parameters entering the potential is usually suitable to describe the frequency of the modes, the time-evolution of signals might present a richer structure, with different behavior in the tail, the presence of new modes (such as massive modes), or even instabilities. All these features are not explicitly exposed by a pure frequency domain analysis and might give hints of new physics. In this paper, we investigate the time evolution of signals considering potentials that slightly deviate from the ones coming from GR, looking into scalar, vector and metric perturbations. We focus on deviations that can be parametrized by a sum of $\sim 1/r^j$ terms in the effective potential, analyzing the effect of each term on the time domain profile.