THE POSITIVITY OF ENERGY FOR ASYMPTOTICALLY ANTI-DESITTER SPACETIMES

We use the formulation of asymptotically anti-de Sitter boundary condi tions given by Ashtekar and Magnon to obtain a coordinate expression f or the general asymptotically AdeS metric in a neighbourhood of infini ty. From this we are able to compute the time delay of null curves pro pagating near infinity. If the gravitational mass is negative, so will be the time delay (relative to null geodesics at infinity) for certai n null geodesics in the spacetime. Following closely an argument given by Penrose, Sorkin, and Woolgar, who treated the asymptotically flat case, we are then able to argue that a negative time delay is inconsis tent with non-negative matter energies in spacetimes having good causa l properties. We thereby obtain a new positive mass theorem for these spacetimes. The theorem may be applied even when the matter flux near the boundary at infinity falls off so slowly that the mass changes, pr ovided the theorem is applied in a time averaged sense. The theorem al so applies in certain spacetimes having local matter-energy that is so metimes negative, as can be the case in semiclassical gravity.