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Proper temperature of Schwarzschild AdS black hole revisited
General Relativity and Quantum Cosmology · Submitted 2 Mar 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Consequently, we show that the free-fall temperature turns out to be real everywhere outside the event horizon without any imaginary value, in particular, it vanishes both at the horizon and at the asymptotic infinity.
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The abstract, sentence by sentence
The Unruh temperature calculated from the global embedding of the Schwarzschild AdS spacetime into Minkowski spacetime was identified with the local temperature measured by a free-fall observer; however, it would be imaginary in a certain region outside the event horizon. So, the temperature was assumed to be zero of no thermal radiation for that region. In this paper, we revisit this issue in the exactly soluble two-dimensional Schwarzschild AdS black hole and present an alternative resolution to this problem by using the Tolman's procedure. However, the process is not straightforward in the sense that one should extend the original procedure to rest upon the traceless energy-momentum tensor in such a way that it could encompass the case of the non-vanishing trace of energy-momentum tensor in the presence of the trace anomaly. Consequently, we show that the free-fall temperature turns out to be real everywhere outside the event horizon without any imaginary value, in particular, it vanishes both at the horizon and at the asymptotic infinity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Unruh temperature calculated from the global embedding of the Schwarzschild AdS spacetime into Minkowski spacetime was identified with the local temperature measured by a free-fall observer; however, it would be imaginary in a certain region outside the event horizon. | background 0.96 | 0.10 | 0.03 | asserted 1.00 |
| s1 | So, the temperature was assumed to be zero of no thermal radiation for that region. | background 0.97 | 0.05 | 0.03 | asserted 0.93 |
| s2 | In this paper, we revisit this issue in the exactly soluble two-dimensional Schwarzschild AdS black hole and present an alternative resolution to this problem by using the Tolman's procedure. | contribution 1.00 | 0.81 | 0.05 | asserted 0.99 |
| s3 | However, the process is not straightforward in the sense that one should extend the original procedure to rest upon the traceless energy-momentum tensor in such a way that it could encompass the case of the non-vanishing trace of energy-momentum tensor in the presence of the trace anomaly. | method 0.88 | 0.43 | 0.04 | asserted 0.88 |
| s4 | Consequently, we show that the free-fall temperature turns out to be real everywhere outside the event horizon without any imaginary value, in particular, it vanishes both at the horizon and at the asymptotic infinity. | result 1.00 | 0.95 | 0.90 | asserted 1.00 |
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The paper
Original abstract
The Unruh temperature calculated from the global embedding of the Schwarzschild AdS spacetime into Minkowski spacetime was identified with the local temperature measured by a free-fall observer; however, it would be imaginary in a certain region outside the event horizon. So, the temperature was assumed to be zero of no thermal radiation for that region. In this paper, we revisit this issue in the exactly soluble two-dimensional Schwarzschild AdS black hole and present an alternative resolution to this problem by using the Tolman's procedure. However, the process is not straightforward in the sense that one should extend the original procedure to rest upon the traceless energy-momentum tensor in such a way that it could encompass the case of the non-vanishing trace of energy-momentum tensor in the presence of the trace anomaly. Consequently, we show that the free-fall temperature turns out to be real everywhere outside the event horizon without any imaginary value, in particular, it vanishes both at the horizon and at the asymptotic infinity.
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How the literature uses it
5 arXiv papers cite this in 7 sentences
What it cites · 17 sentences without a confident label
Uses the method or tool of 3 papers
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Performing the global embedding of the SAdS spacetime into the higher dimensional Minkowski spacetime, a free-fall observer on the SAdS black hole could be identified with the accelerated observer in the higher dimensional Rindler spacetime [ref] , so that the Rindler observer could find the Unruh temperature as [ref] [equation] where $a$ is the proper acceleration of the observer in the higher dimensional Minkowski spacetime.
Accelerated Detectors and Temperature in (Anti) de Sitter Spaces · Proper temperature from the GEMS · 0.97
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Performing the global embedding of the SAdS spacetime into the higher dimensional Minkowski spacetime, a free-fall observer on the SAdS black hole could be identified with the accelerated observer in the higher dimensional Rindler spacetime [ref] , so that the Rindler observer could find the Unruh temperature as [ref] [equation] where $a$ is the proper acceleration of the observer in the higher dimensional Minkowski spacetime.
Taking the Temperature of a Black Hole · Proper temperature from the GEMS · 0.97
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The higher dimensional Minkowski spacetime can be obtained by the following transformation [ref] [equation] where the line element is $ds^2 = η_IJ dX^I dX^J$ with $η_IJ = diag(-1,1,1,1,-1)$.
Mapping Hawking into Unruh Thermal Properties · Proper temperature from the GEMS · 0.96
Compares with 4 papers
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In Sec. [ref], the proper temperature will be obtained in the two-dimensional SAdS black hole by using the GEMS [ref] in the self-contained manner in comparison with our result.
Taking the Temperature of a Black Hole · Introduction · 0.97
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In Sec. [ref], the proper temperature will be obtained in the two-dimensional SAdS black hole by using the GEMS [ref] in the self-contained manner in comparison with our result.
Accelerated Detectors and Temperature in (Anti) de Sitter Spaces · Introduction · 0.97
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In Sec. [ref], the proper temperature will be obtained in the two-dimensional SAdS black hole by using the GEMS [ref] in the self-contained manner in comparison with our result.
Mapping Hawking into Unruh Thermal Properties · Introduction · 0.97
Cites as support 3 papers
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This fact could also be confirmed by showing that the Tolman temperature could vanish effectively at the horizon [ref] .
A Quantal Tolman Temperature · Introduction · 1.00
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For the Schwarzschild black hole, it was shown that the equivalence principle could be restored only at the horizon [ref] , and so it would be natural for the proper temperature to vanish there [ref] .
Hawking radiation, Unruh radiation and the equivalence principle · Conclusion and discussion · 0.99
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For the Schwarzschild black hole, it was shown that the equivalence principle could be restored only at the horizon [ref] , and so it would be natural for the proper temperature to vanish there [ref] .
Hawking versus Unruh effects, or the difficulty of slowly crossing a black hole horizon · Conclusion and discussion · 0.99
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