BHT2 - Self-Graviting Systems (black Rings and Black Strings) |
Speaker_ |
Wiseman, Toby |
Co-autors |
Matt Headrick |
Talk _ |
Ricci flow and black holes |
Abstract _ |
Gradient flow in a potential energy (or action) landscape is a natural way to find paths connecting different saddle points. We apply it to General Relativity, where gradient flow is Ricci flow. We focus on the canonical ensemble for Euclidean gravity in a box, where there are three saddle points: hot flat space and a large and small black hole. Using numerical simulation we find flows connecting the small black hole to the large one and to hot flat space, in the latter case via a topology-changing singularity. In the context of string theory these flows are world-sheet renormalization group trajectories. We also use them to construct a novel free energy diagram for the canonical ensemble, and discuss the use of Ricci flow to numerically solve the vacuum Einstein equations for static black hole solutions. |