Black hole and the adiabatic phase

TL;DR

This paper investigates how slow changes in a Kerr black hole's parameters affect a bound scalar field's energy levels and phase, revealing implications for black hole entropy and quantum states.

Contribution

It introduces the adiabatic phase for scalar fields around Kerr black holes and analyzes the effects of parameter cycles on energy levels and black hole entropy.

Findings

Adiabatic phase and validity conditions derived for scalar fields.

Closed cycles in parameter space affect energy levels of bound states.

Black hole wavefunction acquires a phase related to matter, impacting entropy.

Abstract

An open system consisting of a scalar field bound to a Kerr black hole whose mass ($M$) and specific angular momentum ($a$) are slowly (adiabatically) perturbed is considered. The adiabatically induced phase and the conditions for the validity of the adiabatic approximation are obtained. The effect of closed cycles in parameter space ($a$, $M$ plane) on the energy levels of both stable and unstable scalar field bound states, together with other quantities of interest, is illustrated. Lastly it is noted that the black hole wavefunction will acquire an equal and opposite phase to that of matter thus leading to a change of its effective action (entropy).