*Written by James Lucietti, a Lecturer in Mathematical Physics in the School of Mathematics at the University of Edinburgh; and Carmen Li, previously a graduate student in the School of Mathematics at the University of Edinburgh and now a postdoc in the Institute of Theoretical Physics at the University of Warsaw.*

# How many extreme black holes are there with a given throat geometry?

The classification of equilibrium black hole states is a major open problem in higher dimensional general relativity. Besides being of intrinsic interest, it has numerous applications in modern approaches to quantum gravity and high energy physics. Two key questions to be answered are: *What are the possible topologies and symmetries of a black hole spacetime? What is the ‘moduli’ space of black hole solutions with a given topology and symmetry? *For vacuum gravity in four spacetime dimensions, these questions are answered by the celebrated no-hair theorem which reveals a surprisingly simple answer: the Kerr solution is the only possibility. However, since Emparan and Reall’s discovery of the black ring — an asymptotically flat five dimensional black hole with ‘doughnut’ topology — it has become clear that there is a far richer set of black hole solutions to the higher dimensional Einstein equations.

Over the last decade, a number of general results have been derived which Continue reading