Date/Time
Date(s) - 14/11/2024
3:30 pm - 4:30 pm

Location: Hamilton Hall, Room 312

Speaker: Emma Albertini (Imperial College London)

Title: Towards a uniqueness theorem for static black holes in Kaluza-Klein theory with small circle size

Abstract: Kaluza-Klein theory has a variety of different static black hole solutions and for fixed circle size, multiple solutions with the same mass co-exist. In my talk, I will conjecture that for fixed mass and sufficiently small circle size, the only black holes are the homogeneous ones and I will give evidence that this is indeed the case. Firstly, I will consider a scalar field model with a potential that allows tachyonic behaviour on a product of Minkowski with a circle. This toy model gives an analogous set of static homogeneous and inhomogeneous solutions. I will prove homogeneity of the solutions for small circle size. Turning to the full gravitational theory, I will show that as the circle size becomes small, the solution becomes increasingly homogeneous.

A new approach to uniqueness theorems will be introduced, using Sobolev spaces and elliptic analysis, leading to a local rigidity statement.