Small Black Holes on Cylinders

TL;DR

This paper derives the metric for small black holes on cylindrical spacetimes, analyzes their thermodynamics and binding energy, and discusses implications for black hole phase structures in higher dimensions.

Contribution

It provides the first explicit metric for small black holes on cylinders and calculates their thermodynamic and energetic corrections.

Findings

Thermodynamics deviates from (d+1)-dimensional Schwarzschild black holes.

Leading correction to the relative binding energy is non-zero.

Results have implications for black hole and string phase structures.

Abstract

We find the metric of small black holes on cylinders, i.e. neutral and static black holes with a small mass in d-dimensional Minkowski-space times a circle. The metric is found using an ansatz for black holes on cylinders proposed in hep-th/0204047. We use the new metric to compute corrections to the thermodynamics which is seen to deviate from that of the (d+1)-dimensional Schwarzschild black hole. Moreover, we compute the leading correction to the relative binding energy which is found to be non-zero. We discuss the consequences of these results for the general understanding of black holes and we connect the results to the phase structure of black holes and strings on cylinders.