A Simple Determination of the Thermodynamical Characteristics of the Weakly Charged, Very Thin Black Ring

TL;DR

This paper presents a simple, phenomenological model for the thermodynamical properties of weakly charged, very thin black rings, accurately reproducing key results like entropy and temperature with minimal assumptions.

Contribution

It introduces a straightforward formalism based on horizon circumference quantization that reproduces known thermodynamic characteristics of black rings, simplifying previous complex models.

Findings

Reproduces Bekenstein-Hawking entropy exactly

Matches Hawking temperature for weakly charged black rings

Aligns with prior detailed analyses using a simplified approach

Abstract

In our previous work we suggested a very simple, approximate formalism for description of some basic (especially thermodynamical) characteristics of a non-charged, rotating, very thin black ring. Here, in our new work, generalizing our previous results, we suggest a very simple, approximate description of some basic (especially thermodynamical) characteristics of a weakly charged, rotating, very thin black ring. (Our formalism is not theoretically dubious, since, at it is not hard to see, it can represent an extreme simplification of a more accurate, e.g. 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 weakly charged, rotating, very thin black ring originally obtained earlier using more accurate analysis by Emparan, Aestefanesei, Radu 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 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.