A geometrical framework for the definition of entropy in general relativity via the Nöther 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 a Taub–Bolt solution could not be computed via the Nöther theorem, due to the particular structure of the 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 is sometimes erroneously suggested in the current literature on the subject.
The Entropy of the Taub-Bolt Solution
FATIBENE, Lorenzo;FERRARIS, Marco;FRANCAVIGLIA, Mauro;RAITERI, Marco
2000-01-01
Abstract
A geometrical framework for the definition of entropy in general relativity via the Nöther 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 a Taub–Bolt solution could not be computed via the Nöther theorem, due to the particular structure of the 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 is sometimes erroneously suggested in the current literature on the subject.
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