Vacuum polarization in the Schwarzschild spacetime and dimensional reduction

A. Fabbri; A. Zelnikov; P. Nicolini; P. Sutton; R. Balbinot; V. Frolov

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Vacuum polarization in the Schwarzschild spacetime and dimensional reduction

R. Balbinot, A. Fabbri, V. Frolov, P. Nicolini, P. Sutton, A. Zelnikov

High Energy Physics - Theory · Submitted 6 Dec 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Asymptotic behaviours and analytical approximations are given for $< T_{a b} >$ in the Boulware, Unruh and Hartle-Hawking states.

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arXiv IDhep-th/0012048 (version 2)

Pith IDJV7JM7NO, Pith's permanent record of this paper and its review

CitationA. Fabbri, A. Zelnikov, P. Nicolini, P. Sutton, R. Balbinot, V. Frolov. "Vacuum polarization in the Schwarzschild spacetime and dimensional reduction." arXiv:hep-th/0012048 (2000). https://pith.science/paper/JV7JM7NO

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What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.71 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.12 · mentions code or data availability 0.02.

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A massless scalar field minimally coupled to gravity and propagating in the Schwarzschild spacetime is considered. After dimensional reduction under spherical symmetry the resulting 2D field theory is canonically quantized and the renormalized expectation values $< T_{a b} >$ of the relevant energy-momentum tensor operator are investigated. Asymptotic behaviours and analytical approximations are given for $< T_{a b} >$ in the Boulware, Unruh and Hartle-Hawking states. Special attention is devoted to the black-hole horizon region where the WKB approximation breaks down.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A massless scalar field minimally coupled to gravity and propagating in the Schwarzschild spacetime is considered.	background 0.70	0.39	0.02	asserted 0.84
s1	After dimensional reduction under spherical symmetry the resulting 2D field theory is canonically quantized and the renormalized expectation values $< T_{a b} >$ of the relevant energy-momentum tensor operator are investigated.	method 0.91	0.90	0.08	asserted 0.97
s2	Asymptotic behaviours and analytical approximations are given for $< T_{a b} >$ in the Boulware, Unruh and Hartle-Hawking states.	result 0.83	0.91	0.21	asserted 0.99
s3	Special attention is devoted to the black-hole horizon region where the WKB approximation breaks down.	contribution 0.84	0.73	0.07	asserted 0.89

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

A massless scalar field minimally coupled to gravity and propagating in the Schwarzschild spacetime is considered. After dimensional reduction under spherical symmetry the resulting 2D field theory is canonically quantized and the renormalized expectation values $< T_{a b} >$ of the relevant energy-momentum tensor operator are investigated. Asymptotic behaviours and analytical approximations are given for $< T_{a b} >$ in the Boulware, Unruh and Hartle-Hawking states. Special attention is devoted to the black-hole horizon region where the WKB approximation breaks down.

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References

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Quantum critical collapse in the large $D$ limit
gr-qc 2026-10 conditional novelty 7.0 of 10

Quantum vacuum polarization with Lyapunov exponent D−2 creates a finite-radius trapped surface (quantum wall) in both continuously and discretely self-similar critical collapse at large D.
Quantum fate of the Choptuik naked singularity
gr-qc 2026-06 unverdicted novelty 6.0 of 10

Quantum backreaction generates horizons that cloak the Choptuik naked singularity, reducing its predictability violation to the standard black hole evaporation problem.
The Fate of Nucleated Black Holes in de Sitter Quantum Gravity
hep-th 2026-05 unverdicted novelty 6.0 of 10

Nucleated maximal-mass black holes in de Sitter space undergo thermal Hawking evaporation in smooth quantum states and return fully to the empty de Sitter vacuum.
Inner horizon instability via the trace anomaly effective action
gr-qc 2024-11 conditional novelty 6.0 of 10

The anomaly-induced effective action can reproduce the Hartle-Hawking stress-energy divergence at the Cauchy horizon of Reissner-Nordström, but lacks enough freedom to describe the Unruh state.
Wald-like entropy and Islands in Dimensionally Reduced Einstein-Hilbert Gravity
hep-th 2026-07 conditional novelty 4.0 of 10

Wald-like Noether charge of the DREH plus Polyakov-Liouville action yields the island generalized entropy and unitary Page curves for eternal and quasi-stationary evaporating black holes.

Show 2 more citing papers

Hawking radiation from a semi-classical Schwarzschild black hole
hep-th 2026-05 unverdicted novelty 3.0 of 10

Quantum corrections to Schwarzschild black hole evaporation produce a maximum temperature, radiation cessation, an extremal remnant, and logarithmic entropy correction.
Dilaton Gravity in Two Dimensions
hep-th 2002-04 accept novelty 2.0 of 10

Two-dimensional dilaton gravity can be quantized exactly in its geometric sector, with matter handled perturbatively, and this review assembles the supporting results into a coherent framework.

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8 arXiv papers cite this in 9 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 8 sentences without a confident label

Cites it as background 1 paper

It has long been known theories of gravitation have a much simpler formulation in $$-D [ref] and $$-D [ref] , where associated quantum theories are exactly solvable [ref] .

Primordial Black Hole Evaporation and Spontaneous Dimensional Reduction · Introduction · 0.98

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