  We construct initial data violating the Anti-deSitter Penrose inequality
using scalars with various potentials. Since a version of the Penrose
inequality can be derived from AdS/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 GR techniques to prove the 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 AdS.
