Title: Geometric inequalities for axisymmetric black holes

Abstract: In general relativity, isolated, dynamical black holes arise from asymptotically flat initial data for the Einstein equations. Such data are characterized by invariants such as the ADM mass and angular momentum. When angular momentum is conserved in the evolution, the
standard picture of gravitational collapse suggests an inequality relating the ADM mass and angular momentum. Such geometric inequalities have been rigorously proved for axisymmetric, asymptotically flat maximal initial data for the vacuum Einstein equations. I will discuss recent work on extending this class of inequalities to higher dimensions, where a number of qualitative differences arise (e.g. black holes can have non-spherical horizon topology). In particular, I will discuss how a lower bound for the mass, in terms of a (regularized) harmonic energy functional is obtained.

The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom.  If you would like to attend, please email the organizers for connection details.