Complete integrability of the 5D Einstein vacuum equations: solution generating techniques and other applications

by Pau Figueras (Centre for Particle Theory, Durham)

Tuesday 16 Jun 2009, 14:00 → 15:00 Europe/Zurich

TH Theory Conference Room (CERN)

The Einstein vacuum equations in 5D restricted to solutions with three commuting Killing fields are known to be completely integrable. In this talk, I will exploit this fact to show how one can construct all solutions within this class. As an example, I will explain how to construct a stationary non-extremal vacuum black ring in Taub-NUT. I will comment on the description of this system in terms of D0 and D6 branes in absence of B-fields, and in which the thermal excitations of the D0 branes can be turned on and off. If time allows, as another application of the underlying complete integrability of the Einstein equations, I will show how one can prove uniqueness of the solutions. In particular I will explain how the uniqueness theorems can be extended to extremal black holes.