Cryptographic Censorship

TL;DR

This paper proves a theorem linking pseudorandom evolution in holographic CFTs to the formation of event horizons in the dual bulk spacetime, advancing understanding of cosmic censorship in quantum gravity.

Contribution

It introduces 'Cryptographic Censorship', a novel theorem connecting quantum pseudorandomness to horizon formation, with implications for cosmic censorship and holography.

Findings

Pseudorandom CFT evolution implies event horizon formation.

Classical and semi-Planckian singularities are compatible with pseudorandom evolution.

Naked singularities are unlikely without event horizons under pseudorandom dynamics.

Abstract

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.