Nut Charge, Anti-de Sitter Space and Entropy

TL;DR

This paper tests a proposal that spacetimes with U(1) symmetry have entropy contributions from Misner strings and fixed point sets, confirming the proposal through explicit solutions and matching with boundary CFT entropy in certain limits.

Contribution

Constructs new Taub-Nut-AdS and Taub-Bolt-AdS solutions to verify the entropy contribution from Misner strings, aligning gravitational entropy with boundary CFT predictions.

Findings

Misner string contributions reproduce the gravitational entropy.

Entropy matches boundary CFT predictions in the large squashing limit.

The approach supports the role of Misner strings in black hole thermodynamics.

Abstract

It has been proposed that spacetimes with a U(1) isometry group have contributions to the entropy from Misner strings as well as from the area of $d-2$ dimensional fixed point sets. In this paper we test this proposal by constructing Taub-Nut-AdS and Taub-Bolt-AdS solutions which are examples of a new class of asymptotically locally anti-de Sitter spaces. We find that with the additional contribution from the Misner strings, we exactly reproduce the entropy calculated from the action by the usual thermodynamic relations. This entropy has the right parameter dependence to agree with the entropy of a conformal field theory on the boundary, which is a squashed three-sphere, at least in the limit of large squashing. However the conformal field theory and the normalisation of the entropy remain to be determined.