Light-cone reference for total gravitational energy

Abstract

We give an explicit expression for gravitational energy, written solely in terms of physical spacetime geometry, which (in suitable limits) agrees with the total Arnowitt-Deser-Misner and Trautman-Bondi-Sachs energies for asymptotically flat spacetimes and with the Abbott-Deser energy for asymptotically anti–de Sitter spacetimes. Our expression is a boundary value of the standard gravitational Hamiltonian. Moreover, although it stands alone as such, we derive the expression by picking the zero-point of energy via a “light-cone reference.”