Mass Spectrum for Black Holes in Generic 2-D Dilaton Gravity

TL;DR

This paper presents two independent arguments demonstrating that black hole entropy in generic 2-D dilaton gravity must be quantized, leading to a discrete spectrum consistent across different quantization approaches.

Contribution

It introduces two novel methods for deriving the quantized entropy spectrum of black holes in 2-D dilaton gravity, confirming the spectrum's universality.

Findings

Black hole entropy is quantized as $S= 2 dpi n/G$

Both quantization methods yield the same discrete spectrum

The spectrum is consistent with Dirac quantization results

Abstract

Two arguments for the quantization of entropy for black holes in generic 2-D dilaton gravity are summarized. The first argument is based on reduced quantization of the only physical observables in the theory, namely the black hole mass and its conjugate momentum, the Killing time separation. The second one uses the exact physical mass eigenstates for Euclidean black holes found via Dirac quantization. Both methods give the same spectrum: the black hole entropy must be quantized $S= 2\pi n/G$.