New black holes of vacuum Einstein equations with hyperscaling violation and Nil geometry horizons

TL;DR

This paper introduces a novel five-dimensional vacuum Einstein black hole solution with hyperscaling violation and Nil geometry horizons, revealing unique thermodynamic properties despite negative entropy.

Contribution

It presents the first known vacuum Einstein black hole with Nil geometry horizons and analyzes its thermodynamics using Hamiltonian formalism.

Findings

Positive mass despite negative entropy

First law of thermodynamics holds

Extension to higher dimensions discussed

Abstract

In this paper, we present a new solution of the vacuum Einstein equations in five dimensions which is a static black hole with hyperscaling violation and with a three-dimensional horizon modeled by one the eight Thurston geometries, namely the Nil geometry. This homogeneous geometry is non-trivial in the sense that it is neither of constant curvature nor a product of constant curvature manifolds. Using the Hamiltonian formalism, we identify the mass and entropy of the black hole solution. Curiously enough, in spite of the fact that the entropy turns to be negative, the mass is positive and the first law of thermodynamics holds. We also discuss the extension in higher dimension.