Quasilocal Mass in General Relativity

There have been many attempts to define the notion of quasilocal mass for a spacelike two surface in spacetime by the Hamilton-Jacobi analysis. The essential difficulty in this approach is to identify the right choice of the background configuration to be subtracted from the physical Hamiltonian. Quasilocal mass should be non-negative for surfaces in general spacetime and zero for surfaces in flat spacetime. In this Letter, we propose a new definition of gauge-independent quasilocal mass and prove that it has the desired properties.