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A Quantum Weak Cosmic Censorship and Its Proof

Naman Kumar

Abstract

Recent work has highlighted the deep connection between quantum information and spacetime geometry. Bousso and Shahbazi-Moghaddam (Phys. Rev. Lett. 128, 231301 (2022)) proved that ``hyperentropic'' regions -- where entropy exceeds the area bound -- inevitably lead to singularity formation. In this work, we explore the converse implication: does the thermodynamic consistency of such singularities require them to be hidden? We answer in the affirmative, establishing a Quantum Weak Cosmic Censorship principle governed by Generalized Entropy. This provides a semiclassical mechanism for censorship which forbids naked singularities. Since Quantum Weak Cosmic Censorship is a semiclassical statement, it is more robust than the classical Weak Cosmic Censorship showing naked singularities are forbidden in nature even if quantum effects are taken into account.

A Quantum Weak Cosmic Censorship and Its Proof

Abstract

Recent work has highlighted the deep connection between quantum information and spacetime geometry. Bousso and Shahbazi-Moghaddam (Phys. Rev. Lett. 128, 231301 (2022)) proved that ``hyperentropic'' regions -- where entropy exceeds the area bound -- inevitably lead to singularity formation. In this work, we explore the converse implication: does the thermodynamic consistency of such singularities require them to be hidden? We answer in the affirmative, establishing a Quantum Weak Cosmic Censorship principle governed by Generalized Entropy. This provides a semiclassical mechanism for censorship which forbids naked singularities. Since Quantum Weak Cosmic Censorship is a semiclassical statement, it is more robust than the classical Weak Cosmic Censorship showing naked singularities are forbidden in nature even if quantum effects are taken into account.
Paper Structure (1 section, 5 theorems, 37 equations)

This paper contains 1 section, 5 theorems, 37 equations.

Table of Contents

  1. Sufficient conditions for (A4)

Key Result

Theorem 1

Assume (A1), (A2), and (A3). Then there exists $\lambda_H\in(0,\lambda_*)$ such that i.e. a quantum marginal surface occurs at finite affine parameter before the singular endpoint.

Theorems & Definitions (13)

  • Theorem 1: QMS formation from entropy incompleteness
  • proof
  • Definition 1: Quantum Weak Cosmic Censorship
  • Definition 2: Outermost Quantum Marginal Surface
  • Definition 3: Weak Quantum Trapped Surface (WQTS)
  • Lemma 1: Outermost QMS is weakly quantum trapped
  • proof
  • Proposition 1: Causal sealing of weak quantum trapped surfaces
  • proof
  • Theorem 2: Quantum Weak Cosmic Censorship
  • ...and 3 more