Abstract: I will talk about my recent work (2402.03425) with Netta
Engelhardt, Åsmund Folkestad, Adam Levine, and Evita Verheijden.
We formulate and take two large strides towards proving a quantum
version of the weak cosmic censorship conjecture. We first prove
“Cryptographic Censorship”: a theorem showing that when the time
evolution operator of a holographic CFT is approximately pseudorandom
(or Haar random) on some code subspace, then there must be an event
horizon in the corresponding bulk dual. This result provides a general
condition that guarantees (in finite time) event horizon formation,
with minimal assumptions about the global spacetime structure. Our
theorem relies on an extension of a recent quantum learning no-go
theorem and is proved using new techniques of pseudorandom measure
concentration. To apply this result to cosmic censorship, we separate
singularities into classical, semi-Planckian, and Planckian types. We
illustrate that classical and semi-Planckian singularities are
compatible with approximately pseudorandom CFT time evolution; thus,
if such singularities are indeed approximately pseudorandom, by
Cryptographic Censorship, they cannot exist in the absence of event
horizons. This result provides a sufficient condition guaranteeing
that seminal holographic results on quantum chaos and thermalization,
whose general applicability relies on typicality of horizons, will not
be invalidated by the formation of naked singularities in AdS/CFT.