Quasinormal Modes for Dynamical Black Holes

TL;DR

This paper investigates scalar perturbations and quasinormal modes in dynamical Vaidya black holes, revealing how eigenfrequencies vary at different horizons and demonstrating the effectiveness of the matrix method for precise analysis.

Contribution

It introduces proper boundary conditions for quasinormal modes in dynamical black holes and applies the matrix method for detailed eigenfrequency analysis.

Findings

Eigenfrequencies differ at the apparent horizon and null infinity.

Boundary conditions at null infinity are unaffected by black hole variations in finite time.

Eigenfrequencies evolve slowly following the black hole's mass accretion process.

Abstract

Realistic black holes are usually dynamical, noticeable or sluggish. The Vaidya metric is a significant and tractable model for simulating a dynamical black hole. In this study, we consider scalar perturbations in a dynamical Vaidya black hole, and explore the quasinormal modes by employing the matrix method. We find the proper boundary conditions of the quasinormal modes from physical analysis in the background of a dynamical black hole for the first time. The results show that the eigenfrequencies become different at the apparent horizon and null infinity, because the physical interactions propagate with finite velocity in nature. Any variation of the hole does not affect the boundary condition at null infinity in a finite time. The quasinormal modes originated around the horizon would not immediately come down to, but slowly goes to the final state following the mass accretion process of the hole. The precision of the matrix method is quite compelling, which reveals more details of the eigenfrequencies of the quasinormal mode of perturbations in the Vaidya spacetime.