Quasinormal modes in time-dependent black hole background

TL;DR

This paper investigates the behavior of massless scalar fields in a dynamic charged black hole background, demonstrating that stationary black hole quasinormal mode formulas remain applicable in slowly evolving scenarios, confirming their robustness.

Contribution

It introduces a method to analyze quasinormal modes in time-dependent black holes and shows stationary formulas are effective for slow evolutions.

Findings

Quasinormal mode formulas are robust in slowly evolving black holes.

The generalized tortoise coordinate aids in studying scalar field evolution.

Stationary black hole results approximate time-dependent cases well.

Abstract

We have studied the evolution of the massless scalar field propagating in time-dependent charged Vaidya black hole background. A generalized tortoise coordinate transformation were used to study the evolution of the massless scalar field. It is shown that, for the slowest damped quasinormal modes, the approximate formulae in stationary Reissner-Nordstr\"{o}m black hole turn out to be a reasonable prescription, showing that results from quasinormal mode analysis are rather robust.