Jake Dunn (Imperial College): Toric AdS Black Holes
14:30 – 15:30
In the presence of a negative cosmological constant the maximally symmetric solution to Einstein’s field equations is given by the anti de-Sitter spacetime. Unlike Minkowski space this spacetime has a timelike conformal boundary being not only of interest to physicists through the speculated AdS/CFT correspondence but also to classical relativists due to the additional need of boundary data for well posed problems. In this talk I will discuss a class of spacetimes known as the toric AdS Schwarzschild black hole (TadSS), analogous to the Schwarzschild black hole but with the curiosity of a toroidal symmetry, something not seen in the asymptotically flat case. I will discuss the behaviour of the Klein-Gordon equation on this spacetime under Neumann boundary conditions and use this to motivate the study of the Einstein–Klein-Gordon system within the class of toroidal symmetries again with Neumann data. Here I will prove that for small initial data that spacetime remains close to the TadSS solution and has a complete null infinity.
Tom Johnson (Imperial College): The linear stability of the Schwarzschild solution in the generalised harmonic gauge
16:00 – 17:00
The Schwarzschild solution in general relativity, discovered in 1916, describes a spacetime that contains a non-rotating black hole. A recent (2016) breakthrough paper of Dafermos, Holzegel and Rodnianski showed that the Schwarzschild exterior is linearly stable (in an appropriate sense) as a solution to the vacuum Einstein equations. Their method of proof involved an analysis of the (linearised) Bianchi equations for the Weyl curvature. In this talk, we shall present our proof that the Schwarzschild solution is in fact linearly stable in a generalised harmonic gauge. In particular, we focus on the (linearised) Einstein equations for the metric directly. The result relies upon insights gained for the scalar wave equation by Dafermos and Rodnianski and a fortiori includes a decay statement for solutions to the Zerilli equation. Moreover, the issue of gauge plays an important role in the problem and shall be discussed.