Gravitational surface Hamiltonian and entropy quantization

TL;DR

This paper quantizes the surface Hamiltonian of a gravitational action, demonstrating that black hole horizon entropy is quantized with an equidistant spectrum, consistent across various gravity theories and confirming Bekenstein's area spectrum.

Contribution

It introduces a direct Hamiltonian quantization approach for gravitational horizons, establishing entropy quantization and confirming Bekenstein's area spectrum in a robust manner.

Findings

Horizon entropy is quantized with an equidistant spectrum.

The approach applies to all orders of Lanczos-Lovelock gravity.

The area spectrum aligns with Bekenstein's prediction in general relativity.

Abstract

The surface Hamiltonian corresponding to the surface part of a gravitational action has $xp$ structure where $p$ is conjugate momentum of $x$. Moreover, it leads to $TS$ on the horizon of a black hole. Here $T$ and $S$ are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.