On the notion quasilocal mass in general relativity

          @misc{ pirsa_PIRSA:10050034,
            doi = {10.48660/10050034},
            url = {https://pirsa.org/10050034},
            author = {Wang, Mu-Tao},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {On the notion quasilocal mass in general relativity},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {may},
            note = {PIRSA:10050034 see, \url{https://pirsa.org}}
          }
          

Abstract

There have been many attempts to define quasilocal mass for a spacelike 2-surface in a spacetime by the Hamilton-Jacobi method. The essential difficulty in this approach is the choice of the background configuration to be subtracted from the physical Hamiltonian. The quasilocal mass should be positive for general surfaces, but on the other hand should be zero for surfaces in the flat spacetime. In this talk, I shall describe how to use isometric embeddings into the Minkowski space to overcome this difficulty and propose a new definition of gauge-independent quasi-local mass that has the desired properties, in addition to other natural requirements for a mass. This talk is based on a joint work with Shing-Tung Yau at Harvard.