BTZ black holes from the five-dimensional general relativity with a negative cosmological constant

TL;DR

This paper demonstrates that five-dimensional Einstein gravity with a negative cosmological constant admits solutions combining BTZ black holes with higher genus Riemann surfaces, relevant for string theory and the positive energy conjecture.

Contribution

It shows the existence of BTZ black hole solutions with higher genus Riemann surfaces in five-dimensional AdS gravity, linking to string theory configurations.

Findings

Solutions of the form M_3  M_g exist for g>1.

Spontaneous compactification on Riemann surfaces is possible only for genus > 1.

Connections to near horizon geometries of wrapped D3-branes and the positive energy conjecture.

Abstract

We show that the five-dimensional general relativity with a negative cosmological constant allows the solutions of the form M_3 \times M_g where M_3 is the three-dimensional BTZ black hole and M_g is a higher genus (g>1) Riemann surface with a fixed size. It is shown that this type of spontaneous compactification on a Riemann surface is possible only for the genus larger than one. From type IIB string theory point of view, certain near horizon geometry of D three-branes wrapped on the compact Riemann surface (g>1) is the BTZ (or AdS_3) space-time tensored with the Riemann surface and a constant size five-sphere. The relevance of our analysis to the positive energy conjecture of Horowitz and Myers is discussed.