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.

Latex, 10 pages, 1 figure. Statement of theorem and proof modified. Typos corrected

References in corpus (3)

• Phase Transitions for Flat adS Black Holes
• Precursors, black holes, and a locality bound
• A uniqueness theorem for the adS soliton

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