The Structure of Quantum Singularities on a Cauchy Horizon

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.