Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation

TL;DR

This paper develops time-domain methods based on black-hole perturbation theory to calculate how black holes absorb mass and angular momentum from gravitational waves, especially in small or slow-motion scenarios.

Contribution

It introduces two practical prescriptions for absorption calculations in the time domain, applicable to both rotating and nonrotating black holes, and derives explicit formulas in the small-hole/slow-motion approximation.

Findings

Formulas for mass and angular momentum absorption in the time domain.

Explicit analytical expressions for small or slowly moving black holes.

Application of formalism to tidal interactions with external gravitational fields.

Abstract

The first objective of this work is to obtain practical prescriptions to calculate the absorption of mass and angular momentum by a black hole when external processes produce gravitational radiation. These prescriptions are formulated in the time domain within the framework of black-hole perturbation theory. Two such prescriptions are presented. The first is based on the Teukolsky equation and it applies to general (rotating) black holes. The second is based on the Regge-Wheeler and Zerilli equations and it applies to nonrotating black holes. The second objective of this work is to apply the time-domain absorption formalisms to situations in which the black hole is either small or slowly moving. In the context of this small-hole/slow-motion approximation, the equations of black-hole perturbation theory can be solved analytically, and explicit expressions can be obtained for the absorption of mass and angular momentum. The changes in the black-hole parameters can then be understood in terms of an interaction between the tidal gravitational fields supplied by the external universe and the hole's tidally-induced mass and current quadrupole moments. For a nonrotating black hole the quadrupole moments are proportional to the rate of change of the tidal fields on the hole's world line. For a rotating black hole they are proportional to the tidal fields themselves.