A Microscopic Model for the Black hole - Black string Phase Transition

Computations in general relativity have revealed an interesting phase diagram for the black hole - black string phase transition, with three different black objects present for a range of mass values. We can add charges to this system by `boosting' plus dualities; this makes only kinematic changes in the gravity computation but has the virtue of bringing the system into the near-extremal domain where a microscopic model can be conjectured. When the compactification radius is very large or very small then we get the microscopic models of 4+1 dimensional near-extremal holes and 3+1 dimensional near-extremal holes respectively (the latter is a uniform black string in 4+1 dimensions). We propose a simple model that interpolates between these limits and reproduces most of the features of the phase diagram. These results should help us understand how `fractionation' of branes works in general situations.