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<p>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 ⟨<i>T</i><sub><i>μν</i></sub>⟩ — 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.</p><p>Here, I highlight a mildness puzzle of Cauchy horizon singularities: the ⟨<i>T</i><sub><i>μν</i></sub>⟩ singularity is significantly milder than expected from symmetry and dimensional analysis. I address the puzzle in a simple spacetime <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">W</mi> <mi>P</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{W}}_P \)</EquationSource> </InlineEquation>, 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 <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">W</mi> <mi>P</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{W}}_P \)</EquationSource> </InlineEquation>, gives rise to a universal mild singularity structure for <i>robust singularities</i>, ones whose leading singular behavior is state-independent. I make non-trivial predictions for <i>all</i> black hole Cauchy horizon singularities using this, and discuss extending the results beyond robust singularities and the strict near Cauchy horizon limit.</p>

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The structure of quantum singularities on a Cauchy horizon

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  • 发表日期：

    2025年7月22日

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  • Arvin Shahbazi-Moghaddam

摘要

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 ⟨Tμν⟩ — 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 ⟨Tμν⟩ singularity is significantly milder than expected from symmetry and dimensional analysis. I address the puzzle in a simple spacetime W P \( {\mathcal{W}}_P \) , 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 \( {\mathcal{W}}_P \) , 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.