On the Entropy of Quantum Fields in Black Hole Backgrounds

N. Ohta; S. P. de Alwis

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On the Entropy of Quantum Fields in Black Hole Backgrounds

S. P. de Alwis, N. Ohta

High Energy Physics - Theory · Submitted 3 Dec 1994

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

The authors' main claim We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral in the original metric is a Liouville type action.

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We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral in the original metric is a Liouville type action. A general formula for the free energy is derived in the high temperature approximation and applied to various cases. In particular we find that thermodynamics in the extremal Reissner-Nordstr\"om space has extra singularities that make it ill-defined.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral in the original metric is a Liouville type action.	contribution 0.69	0.93	0.41	asserted 1.00
s1	A general formula for the free energy is derived in the high temperature approximation and applied to various cases.	method 0.55	0.95	0.12	asserted 1.00
s2	In particular we find that thermodynamics in the extremal Reissner-Nordstr\"om space has extra singularities that make it ill-defined.	result 1.00	0.93	0.32	asserted 1.00

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The paper

Original abstract

We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral in the original metric is a Liouville type action. A general formula for the free energy is derived in the high temperature approximation and applied to various cases. In particular we find that thermodynamics in the extremal Reissner-Nordstr\"om space has extra singularities that make it ill-defined.

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References

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Cited by 2 Pith papers

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

Black Hole Entropy and Entropy of Entanglement
hep-th 1995-03 conditional novelty 6.0 of 10

For scalar and spin-half fields the one-loop black hole entropy equals the entanglement entropy, but for an Abelian gauge field the two differ by a horizon-localized contact term with no thermal or state-counting inte...
Entanglement entropy of black holes
hep-th 2011-04 accept novelty 2.0 of 10

A systematic review showing that the conical-singularity method computes black hole entanglement entropy whose UV divergences renormalize Newton's constant and quadratic curvature couplings, while non-minimally couple...

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4 arXiv papers cite this in 6 sentences

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Papers citing it · 3 sentences without a confident label

Uses its method or tool 1 paper

This is the so-called optical geometry of [ref] , applied in this context in [ref] .[The change of frame corresponds to a change in integration measure which, as discussed in [ref] , produces an anomalous term in the effective action that doesn't affect the entropy.

Extractable entanglement from a Euclidean hourglass · Hourglass prescription in higher dimensions · 0.83

Cites it as support 1 paper

But this is a local change in integration measure which, as discussed in [ref] , produces a Liouville action that doesn't affect the entropy.[Intuitively the change in integration measure, being local, shifts the effective action by a term proportional to $β$ and hence does not affect the entropy. ] So for our purposes the fluctuation determinants cancel.

Defining entanglement without tensor factoring: a Euclidean hourglass prescription · Covariant gauge · 1.00

Cites it as background 1 paper

The Euclidean path integral approach in the optical metric was considered in [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] .

Entanglement entropy of black holes · Euclidean path integral approach in terms of optical metric · 0.96

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