Positive Mass from Holographic Causality

TL;DR

This paper demonstrates that causality constraints on the boundary in holographic duals ensure positive mass in asymptotically AdS spacetimes for dimensions greater than two, without needing local energy conditions.

Contribution

It proves positivity of mass from boundary causality in holographic duals, extending previous results by removing local energy condition assumptions.

Findings

Causality on the boundary implies positive mass in the bulk.

Generalized time-delay formula relates boundary causality to bulk mass.

Discussion of negative mass AdS soliton and energy conjecture.

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.