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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| Format: | Article |
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Springer Verlag
2018
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| Online Access: | https://eprints.nottingham.ac.uk/52386/ |
| _version_ | 1848798714194296832 |
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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. |
| first_indexed | 2025-11-14T20:24:09Z |
| format | Article |
| id | nottingham-52386 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:24:09Z |
| publishDate | 2018 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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/ |