We construct initial data violating the anti–de Sitter Penrose inequality using scalars with various potentials. Since a version of the Penrose inequality can be derived from $\mathrm{AdS}/\mathrm{CFT}$, we argue that it is a new swampland condition, ruling out holographic UV completion for theories that violate it. We produce exclusion plots on scalar couplings violating the inequality, and we find no violations for potentials from string theory. In the special case where the dominant energy condition holds, we use general relativity techniques to prove the anti–de Sitter (AdS) Penrose inequality in all dimensions, assuming spherical, planar, or hyperbolic symmetry. However, our violations show that this result cannot be generically true with only the null energy condition, and we give an analytic sufficient condition for violation of the Penrose inequality, constraining couplings of scalar potentials. Like the Breitenlohner-Freedman bound, this gives a necessary condition for the stability of asymptotically AdS (AAdS) spacetimes.

• Received 28 September 2022
• Revised 13 January 2023
• Accepted 7 March 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.121501

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Published by the American Physical Society