Disturbing the Black Hole

TL;DR

The paper explores the idea that the horizon area of near equilibrium black holes remains nearly constant during slow changes, supporting a potential scheme for black hole quantization.

Contribution

It provides examples and conditions supporting the conjecture that black hole horizon area is an adiabatic invariant, aiding in the development of black hole quantization schemes.

Findings

Horizon area remains nearly invariant under quasistatic perturbations.

Scalar field interactions can be consistent with adiabatic invariance.

The results support the conjecture for specific black hole perturbations.

Abstract

I describe some examples in support of the conjecture that the horizon area of a near equilibrium black hole is an adiabatic invariant. These include a Schwarzschild black hole perturbed by quasistatic scalar fields (which may be minimally or nonminimally coupled to curvature), a Kerr black under the influence of scalar radiation at the superradiance treshold, and a Reissner--Nordstr\"om black hole absorbing a charge marginally. These clarify somewhat the conditions under which the conjecture would be true. The desired ``adiabatic theorem'' provides an important motivation for a scheme for black hole quantization.