Quantum fields during black hole formation: how good an approximation is the Unruh state?

We study the quantum effects of a test Klein-Gordon field in a Vaidya space-time consisting of a collapsing null shell that forms a Schwazschild black hole, by explicitly obtaining, in a (1 + 1)-dimensional model, the Wightman function, the renormalised stress-energy tensor, and by analysing particl...

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Main Authors: Juárez-Aubry, Benito A., Louko, Jorma
Format: Article
Published: Springer Verlag 2018
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Online Access:https://eprints.nottingham.ac.uk/52386/
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author Juárez-Aubry, Benito A.
Louko, Jorma
author_facet Juárez-Aubry, Benito A.
Louko, Jorma
author_sort Juárez-Aubry, Benito A.
building Nottingham Research Data Repository
collection Online Access
description We study the quantum effects of a test Klein-Gordon field in a Vaidya space-time consisting of a collapsing null shell that forms a Schwazschild black hole, by explicitly obtaining, in a (1 + 1)-dimensional model, the Wightman function, the renormalised stress-energy tensor, and by analysing particle detector rates along stationary orbits in the exterior black hole region, and make a comparison with the folklore that the Unruh state is the state that emerges from black hole formation. In the causal future of the shell, we find a negative ingoing flux at the horizon that agrees precisely with the Unruh state calculation, and is the source of black hole radiation, while in the future null infinity we find that the radiation flux output in the Unruh state is an upper bound for the positive outgoing flux in the collapsing null shell spacetime. This indicates that back-reaction estimates based on Unruh state calculations over-estimate the energy output carried by so-called pre-Hawking radiation. The value of the output predicted by the Unruh state is however approached exponentially fast. Finally, we find that at late times, stationary observers in the exterior black hole region in the collapsing shell spacetime detect the local Hawking temperature, which is also well characterised by the Unruh state, coming from right-movers. Early-time discrepancies between the detector rates for the Unruh state and for the state in the collapsing shell spacetime are explored numerically.
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spelling nottingham-523862020-05-04T19:37:32Z https://eprints.nottingham.ac.uk/52386/ Quantum fields during black hole formation: how good an approximation is the Unruh state? Juárez-Aubry, Benito A. Louko, Jorma We study the quantum effects of a test Klein-Gordon field in a Vaidya space-time consisting of a collapsing null shell that forms a Schwazschild black hole, by explicitly obtaining, in a (1 + 1)-dimensional model, the Wightman function, the renormalised stress-energy tensor, and by analysing particle detector rates along stationary orbits in the exterior black hole region, and make a comparison with the folklore that the Unruh state is the state that emerges from black hole formation. In the causal future of the shell, we find a negative ingoing flux at the horizon that agrees precisely with the Unruh state calculation, and is the source of black hole radiation, while in the future null infinity we find that the radiation flux output in the Unruh state is an upper bound for the positive outgoing flux in the collapsing null shell spacetime. This indicates that back-reaction estimates based on Unruh state calculations over-estimate the energy output carried by so-called pre-Hawking radiation. The value of the output predicted by the Unruh state is however approached exponentially fast. Finally, we find that at late times, stationary observers in the exterior black hole region in the collapsing shell spacetime detect the local Hawking temperature, which is also well characterised by the Unruh state, coming from right-movers. Early-time discrepancies between the detector rates for the Unruh state and for the state in the collapsing shell spacetime are explored numerically. Springer Verlag 2018-05-23 Article PeerReviewed Juárez-Aubry, Benito A. and Louko, Jorma (2018) Quantum fields during black hole formation: how good an approximation is the Unruh state? Journal of High Energy Physics, 2018 (5). p. 140. ISSN 1029-8479 Black Holes Field Theories in Lower Dimensions https://link.springer.com/article/10.1007%2FJHEP05%282018%29140 doi:10.1007/JHEP05(2018)140 doi:10.1007/JHEP05(2018)140
spellingShingle Black Holes
Field Theories in Lower Dimensions
Juárez-Aubry, Benito A.
Louko, Jorma
Quantum fields during black hole formation: how good an approximation is the Unruh state?
title Quantum fields during black hole formation: how good an approximation is the Unruh state?
title_full Quantum fields during black hole formation: how good an approximation is the Unruh state?
title_fullStr Quantum fields during black hole formation: how good an approximation is the Unruh state?
title_full_unstemmed Quantum fields during black hole formation: how good an approximation is the Unruh state?
title_short Quantum fields during black hole formation: how good an approximation is the Unruh state?
title_sort quantum fields during black hole formation: how good an approximation is the unruh state?
topic Black Holes
Field Theories in Lower Dimensions
url https://eprints.nottingham.ac.uk/52386/
https://eprints.nottingham.ac.uk/52386/
https://eprints.nottingham.ac.uk/52386/