The Entropy of Taub-Bolt Solution

TL;DR

This paper applies a Noether theorem-based geometric framework to compute the entropy of Taub-Bolt solutions in General Relativity, challenging previous beliefs about the limitations of this approach and clarifying the role of singularities.

Contribution

It demonstrates that the Noether theorem can be used to compute the entropy of Taub-Bolt solutions, including contributions from singularities like the Misner string.

Findings

Entropy computed matches known results from statistical methods.

The entropy does not follow the one-quarter area law.

Entropy is not solely determined by horizons, involving singularities.

Abstract

A geometrical framework for the definition of entropy in General Relativity via Noether theorem is briefly recalled and the entropy of Taub-Bolt Euclidean solutions of Einstein equations is then obtained as an application. The computed entropy agrees with previously known results, obtained by statistical methods. It was generally believed that the entropy of Taub-Bolt solution could not be computed via Noether theorem, due to the particular structure of singularities of this solution. We show here that this is not true. The Misner string singularity is, in fact, considered and its contribution to the entropy is analyzed. As a result, in our framework entropy does not obey the "one-quarter area law" and it is not directly related to horizons, as sometimes erroneously suggested in current literature on the subject.