Small Black Holes on Cylinders

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.