Local foliations by critial surfaces of the Hawking energy and small sphere limit

05.05.2022, 14:00-15:30  –  C6H05 Tübingen, 2.09.2.22 Campus Golm
Geometric Analysis, Differential Geometry and Relativity

Alejandro Penuela Diaz

The Hawking energy is one of the most famous local energies in general relativity, by using a Lyapunov Schmidt reduction procedure we construct  unique  local foliations of critical surfaces of the Hawking energy on initial data sets (spacelike hypersurfaces in a spacetime), and  we show  a nonexistence condition. 

Any quasilocal energy should satisfy the so called small sphere limit, therefore we also discuss the relation of these surfaces and the small sphere limit. In particular we discuss some discrepancies on the small sphere limit, so when approaching a point with these foliations and when approaching as in the small sphere limit.