Black hole size and phase space volumes

Understand

For extremal black holes the fuzzball conjecture says that the throat of the geometry ends in a quantum `fuzz', instead of being infinite in length with a horizon at the end.

• For the D1-D5 system we consider a family of sub-ensembles of states, and find that in each case the boundary area of the fuzzball satisfies a Bekenstein type relation with the entropy enclosed.
• We suggest a relation between the `capped throat' structure of microstate geometries and the fact that the extremal hole was found to have zero entropy in some gravity computations.
• We examine quantum corrections including string 1-loop effects and check that they do not affect our leading order computations.