Positive Mass from Holographic Causality

For ($n+1$)-dimensional asymptotically anti–de Sitter (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 $n\ge 3$, without the assumption of any local energy condition. We make crucial use of a time-delay formula relating the Ashtekar-Magnon mass of the spacetime to the time delay of a bulk null curve relative to that of a boundary null geodesic. We also discuss holographic causality for the negative mass AdS soliton and its implications for the positive energy conjecture of Horowitz and Myers.