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

Understand

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.