Curvature, Phase Space, Holography and Black Hole Entropy

TL;DR

This paper explores the relationship between black hole entropy, curvature, and holography, proposing a unified framework that incorporates phase space and quantum effects to better understand Hawking radiation across all black hole types.

Contribution

It introduces a unified perspective linking black hole entropy, curvature, and holography, including phase space considerations and quantum principles, applicable to all black hole masses and dimensions.

Findings

Volume inside the horizon influences Hawking flux.

Holography implies a phase space quantum filled with one photon.

Generalized uncertainty principle can be integrated into the framework.

Abstract

This paper discusses the thermodynamics of a black hole with respect to Hawking radiation and the entropy. We look at a unified picture of black hole entropy and curvature and how this can lead to the usual black hole luminosity due to Hawking radiation. It is also shown how the volume inside the horizon, apart from surface area, can play a role in understanding the Hawking flux. In addition holography also implies a phase space associated with the interior volume and this happens to be just a quantum of phase space, filled with just one photon. Generalised uncertainty principle can be incorporated in this analysis. These results hold for all black hole masses in any dimensions.