Positive Mass from Holographic Causality

Abstract

For n+1 dimensional asymptotically AdS spacetimes which have holographic duals on their n dimensional conformal boundaries, we show that the imposition of causality on the boundary theory is sufficient to prove positivity of mass for the spacetime when n > 2, without the assumption of any local energy condition. We make crucial use of a generalization of the time-delay formula calculated in gr-qc/9404019, which relates the time delay of a bulk null curve with respect to a boundary null geodesic to the Ashtekar-Magnon mass of the spacetime. We also discuss holographic causality for the negative mass AdS soliton and its implications for the positive energy conjecture of Horowitz and Myers.