Holographic Time Crystals vs Penrose

TL;DR

This paper investigates the theoretical possibility of thermal time crystals in holographic conformal field theories, explores their connection to black hole geometries, and examines the Penrose inequality's role as a potential Swampland constraint.

Contribution

It demonstrates that holographic time crystals would violate the Penrose inequality unless the positive mass theorem holds, and discovers neutral hairy black holes in M-theory that challenge existing no-hair conjectures.

Findings

Holographic time crystals likely require non-zero angular momentum.

Neutral hairy black holes exist in M-theory with boundary conditions respecting conformal invariance.

Penrose inequality holds iff the positive mass theorem holds in spherical symmetry.

Abstract

In the large$-N$ limit, no known no-go theorem rules out thermal time crystals that spontaneously break continuous time-translation, unlike in the large volume limit. If thermal time crystals exist in holographic CFTs, they would correspond to ensemble-dominating black holes with eternally time-varying exterior geometries. We point out that recent work on a conjectured non-linear instability of slowly rotating Kerr-AdS$_4$ produced viable candidates for such states. Then we show that the existence of holographic microcanonical time crystals would imply violations of the AdS Penrose inequality (PI). We proceed to look for violations of the PI in spherical symmetry, working with Einstein-scalar gravity with the most general possible boundary conditions compatible with boundary conformal invariance. We derive a set of ODEs for maximally PI-violating initial data. Solving these numerically, we find strong evidence that in the particular case of spherical symmetry, the PI holds iff the positive mass theorem (PMT) holds. This suggests that holographic CFT$_3$ time crystals can only possibly exist at non-zero angular momentum, at least in the absence of electric charge. We also discover neutral hairy black holes in a consistent truncation of M-theory that has a PMT and boundary conditions respecting conformal invariance, disproving an existing no-hair conjecture. Finally, we show that previous PI-violating solutions by the author all existed in theories where the PMT is violated. Unfortunately, our results imply that there currently are no known examples where the PI functions as a non-trivial Swampland constraint.