Perturbations of the Vaidya metric in the frequency domain: Quasi-normal modes and tidal response

TL;DR

This paper analyzes how linear perturbations behave on a Vaidya black hole background with evolving mass, computing quasi-normal modes and tidal responses in the frequency domain, which has implications for gravitational wave signals.

Contribution

It provides the first explicit computation of quasi-normal modes and tidal Love numbers for a Vaidya black hole with a constant mass change rate.

Findings

Explicit quasi-normal mode spectrum derived

Tidal Love numbers calculated for evolving mass

Frequency domain analysis applied to time-dependent background

Abstract

The mass of a black hole can dynamically evolve due to various physical processes, such as for instance accretion, Hawking radiation, absorption of gravitational/electromagnetic waves, superradiance, etc. This evolution can have an impact on astrophysical observables, like the ringdown gravitational signal. An effective description of a spherically symmetric black hole with evolving mass is provided by the Vaidya metric. In our investigation, we explore the dynamics of linear perturbations on this background, assuming a constant rate of change for the mass. Despite the time-dependent background, a judicious change of coordinates allows us to treat the perturbations in the frequency domain, and to compute explicitly the quasi-normal modes and the tidal Love numbers.