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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Maths HEP Lunchtime Seminars: Ricci flow and black holes

Presented by Toby Wiseman, Imperial

3 November 2006 13:00 in CM221

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.

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