A Simple Determination of the Thermodynamical Characteristics of a Very Thin Black Ring

TL;DR

This paper introduces a simple, phenomenological model for the thermodynamics of very thin rotating black rings, accurately reproducing key properties like entropy and temperature with minimal assumptions.

Contribution

It proposes a straightforward formalism based on horizon circumference quantization that matches complex prior results for black ring thermodynamics.

Findings

Reproduces Bekenstein-Hawking entropy exactly

Matches Hawking temperature from detailed analyses

Aligns with Bekenstein quantization of entropy and horizon area

Abstract

In this work we suggest a very simple, approximate formalism for description of some basic (especially thermodynamical) characteristics of a rotating, very thin black ring. (In fact, our formalism is not theoretically dubious, since, at it is not hard to see, it can correspond to an extreme simplification of a more accurate, Copeland-Lahiri string formalism for the black hole description.) Even if suggested formalism is, generally speaking, phenomenological and rough, obtained final results, unexpectedly, are non-trivial. Concretely, given formalism reproduces exactly Bekenstein-Hawking entropy, Bekenstein quantization of the entropy or horizon area and Hawking temperature of a rotating, very thin black ring obtained earlier using more accurate analysis by Reall, Emparan, Elvang, Virmani etc. (Conceptually it is similar to situation in Bohr's atomic model where energy levels are determined practically exactly even if electron motion is described roughly.) Our formalism, according to suggestions in our previous works, is physically based on the assumption that circumference of the horizon tube holds the natural (integer) number of corresponding reduced Compton's wave length. (It is conceptually similar to Bohr's quantization postulate in Bohr's atomic model interpreted by de Broglie relation.) Also, we use, mathematically, practically only simple algebraic equations (by determination of Hawking temperature we use additionally only simple differentiation of Smarr relation).