Quantum Black Holes as Atoms

TL;DR

This paper explores the analogy between black holes and atoms, proposing a discrete, uniformly spaced spectrum for black hole mass levels, which could lead to observable deviations from Hawking radiation predictions.

Contribution

It reviews physical and formal arguments for a discrete black hole spectrum, discusses its implications for radiation and entropy, and presents an algebraic framework for black hole observables.

Findings

Black hole mass spectrum may be discrete and uniformly spaced.

The spectrum could distort the semiclassical Hawking radiation.

Black hole entropy implies exponential degeneracy of levels.

Abstract

In some respects the black hole plays the same role in gravitation that the atom played in the nascent quantum mechanics. This analogy suggests that black hole mass $M$ might have a discrete spectrum. I review the physical arguments for the expectation that black hole horizon area eigenvalues are uniformly spaced, or equivalently, that the spacing between stationary black hole mass levels behaves like 1/M. This sort of spectrum has also emerged in a variety of formal approaches to black hole quantization by a number of workers (with some notable exceptions). If true, this result indicates a distortion of the semiclassical Hawking spectrum which could be observable even for macroscopic black holes. Black hole entropy suggests that the mentioned mass levels should be degenerate to the tune of an exponential in $M^2$, as first noted by Mukhanov. This has implications for the statistics of the radiation. I also discuss open questions: whether radiative decay will spread the levels beyond recognition, whether extremal black holes can be described by this scheme, etc. I then describe an elementary algebra for the relevant black hole observables, an outcome of work by Mukhanov and myself, which reproduces the uniformly spaced area spectrum.