The Structure of Quantum Singularities on a Cauchy Horizon

TL;DR

This paper investigates the nature of quantum singularities at Cauchy horizons in black holes, proposing a broad quantum field theory framework that explains their universal mildness and predicts their behavior.

Contribution

It introduces a novel QFT construction that accounts for the universal mild singularity structure at Cauchy horizons, advancing understanding of quantum effects in black hole spacetimes.

Findings

Cauchy horizon singularities are milder than expected from symmetry considerations.

A universal singularity structure is predicted for robust singularities near Cauchy horizons.

The framework reproduces known horizon singularities and extends to new predictions.

Abstract

Spacetime singularities pose a long-standing puzzle in quantum gravity. Unlike Schwarzschild, a generic family of black holes gives rise to a Cauchy horizon on which, even in the Hartle-Hawking state, quantum observables such as $\langle T_{\mu\nu} \rangle$ -- the expectation value of the stress-energy tensor -- can diverge, causing a breakdown of semiclassical gravity. Because they are diagnosed within quantum field theory (QFT) on a smooth background, these singularities may provide a better-controlled version of the spacetime singularity problem, and merit further study. Here, I highlight a mildness puzzle of Cauchy horizon singularities: the $\langle T_{\mu\nu} \rangle$ singularity is significantly milder than expected from symmetry and dimensional analysis. I address the puzzle in a simple spacetime $W_P$, which arises universally near all black hole Cauchy horizons: the past of a codimension-two spacelike plane in flat spacetime. Specifically, I propose an extremely broad QFT construction in which, roughly speaking, Cauchy horizon singularities originate from operator insertions in the causal complement of the spacetime. The construction reproduces well-known outer horizon singularities (e.g., in the Boulware state), and remarkably, when applied to $W_P$, gives rise to a universal mild singularity structure for robust singularities, ones whose leading singular behavior is state-independent. I make non-trivial predictions for all black hole Cauchy horizon singularities using this, and discuss extending the results beyond robust singularities and the strict near Cauchy horizon limit.