Black hole area quantization

TL;DR

This paper demonstrates the equivalence of two different formalisms for black hole area quantization, predicting a Planck-sized remnant for non-rotating, neutral black holes across spacetime dimensions.

Contribution

It establishes the equivalence between the reduced phase space and algebraic approaches to black hole area quantization, introducing operators that unify the formalisms.

Findings

Approaches are equivalent for non-rotating, neutral black holes in any dimension.

Mapping predicts a Planck size remnant.

Unified operators express dynamical variables in both formalisms.

Abstract

It has been argued by several authors that the quantum mechanical spectrum of black hole horizon area must be discrete. This has been confirmed in different formalisms, using different approaches. Here we concentrate on two approaches, the one involving quantization on a reduced phase space of collective coordinates of a Black Hole and the algebraic approach of Bekenstein. We show that for non-rotating, neutral black holes in any spacetime dimension, the approaches are equivalent. We introduce a primary set of operators sufficient for expressing the dynamical variables of both, thus mapping the observables in the two formalisms onto each other. The mapping predicts a Planck size remnant for the black hole.