Revisit the small sphere limits of Wang-Yau quasi-local mass

Ye-Kai Wang

Department of Mathematics

National Cheng Kung University

ykwang@mail.ncku.edu.tw

A fundamental problem in general relativity is to measure the energy of gravitational field in an extended but finite region. The Wang-Yau quasi-local mass is proposed in 2008 to tackle the problem. Besides positivity, theWang-Yau quasi-local mass verifies various classical limits: It recovers ADM mass, Bondi-Sachs energy-momentum for large spheres at spatial infinity and null infinity, and Bel-Robinson tensor for small spheres in vacuum spacetimes. In this talk, we present another approach to the small sphere limits using the idea from the proof of positive mass theorem. This is a joint work with Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau.