Lightcone reference for total gravitational energy∗

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 Abbot-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 “lightcone reference.” Chapel Hill, 10 March 1999 ∗ gr-qc/yyymmnn, TAR-067-UNC †[email protected]