From Quantum Information to Cosmic Censorship: Emergent Spacetimes and Their Surfaces

Abstract

In this thesis, we explore classical and semiclassical gravity from the perspective of the AdS/CFT correspondence. We leverage global methods in General Relativity (GR) together with quantum information- and complexity-theoretic properties of the conformal field theory (CFT) dual to obtain novel results in classical and semiclassical gravity.

In the first part, we obtain a collection of results suggesting that holography enforces a refined version of Cosmic Censorship that potentially can replace the Weak Cosmic Censorship (WCC) conjecture, which has been disproven in Anti-de Sitter (AdS) spacetimes. We show that certain important GR results usually proven assuming WCC can instead be derived from consistency of the AdS/CFT dictionary. We also construct new likely violations of WCC in asymptotically AdS₄ spacetimes, but show that these cannot have a holographic dual; this provides evidence that singularities are better behaved in holographic theories, compared to GR with generic matter. Finally, we show a connection between event horizons and CFT pseudorandomness, and we construct a new measure of the size of a naked singularity. We conjecture that quantum gravity only forbids macroscopic naked singularities, according to this measure.

In the second part, we derive new properties of various extremal submanifolds, with several consequences for AdS/CFT. For example, we provide a physically intuitive explanation for why extremal surfaces are natural boundaries between independent subsystems. We also prove results that constrain far-from-equilibrium dynamics in gravity and CFTs. Finally, we construct a puzzle showing that geometric states with large entanglement need not correspond to a wormhole, highlighting subtleties in the ER=EPR proposal.