Backreaction of Mass and Angular Momentum Accretion on Black Holes: General Formulation of the Metric Perturbations and Application to the Blandford-Znajek Process

TL;DR

This paper develops a formalism for analyzing how mass and angular momentum accretion affect black hole metrics, applying it to the Blandford-Znajek process to connect perturbations with energy extraction and horizon dynamics.

Contribution

It introduces a general framework for metric perturbations due to accretion and applies it to model the time evolution of black hole parameters in the Blandford-Znajek process.

Findings

Time-dependent monopole and dipole perturbations correspond to a slowly rotating Kerr metric.

Black hole mass decreases and horizon area increases during energy extraction.

The formalism links perturbations to black hole mechanics and energy flow.

Abstract

We study the metric backreaction of mass and angular momentum accretion on black holes. We first develop the formalism of monopole and dipole linear gravitational perturbations around the Schwarzschild black holes in the Eddington-Finkelstein coordinates against the generic time-dependent matters. We derive the relation between the time dependence of the mass and angular momentum of the black hole and the energy-momentum tensors of accreting matters. As a concrete example, we apply our formalism to the Blandford-Znajek process around the slowly rotating black holes. We find that the time dependence of the monopole and dipole perturbations can be interpreted as the slowly rotating Kerr metric with time-dependent mass and spin parameters, which are determined from the energy and angular momentum extraction rates of the Blandford-Znajek process. We also show that the Komar angular momentum and the area of the apparent horizon are decreasing and increasing in time, respectively, while they are consistent with the Blandford-Znajek argument of energy extraction in term of black hole mechanics if we regard the time-dependent mass parameter as the energy of the black hole.