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.