Microscopic Origin of Bekenstein-Hawking Entropy in $(2+1)$ Gravity: A Thermo Field Dynamics Approach
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918357128708096 |
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| author | C., W. A. Rojas S, J. R. Arenas |
| author_facet | C., W. A. Rojas S, J. R. Arenas |
| contents | We compute the entanglement entropy of a real massive scalar field near a non-rotating BTZ black hole using Thermo Field Dynamics. Modeling the black hole as a collapsing dust shell in AdS3, we derive the shell trajectory R(t) as seen by a Fiducial Observer (FIDO). From the Hartle-Hawking and Killing-Boulware vacua, we obtain the Wightman function difference and compute energy density, revealing a sharply localized energy density just outside the horizon, consistent with the brick wall picture. A full thermodynamic analysis yields an entanglement entropy proportional to the horizon area, numerically matching the Bekenstein-Hawking entropy. All intermediate steps, including junction conditions, Kruskal extension, WKB modes, and UV regularization, are explicitly detailed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22360 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Microscopic Origin of Bekenstein-Hawking Entropy in $(2+1)$ Gravity: A Thermo Field Dynamics Approach C., W. A. Rojas S, J. R. Arenas General Relativity and Quantum Cosmology We compute the entanglement entropy of a real massive scalar field near a non-rotating BTZ black hole using Thermo Field Dynamics. Modeling the black hole as a collapsing dust shell in AdS3, we derive the shell trajectory R(t) as seen by a Fiducial Observer (FIDO). From the Hartle-Hawking and Killing-Boulware vacua, we obtain the Wightman function difference and compute energy density, revealing a sharply localized energy density just outside the horizon, consistent with the brick wall picture. A full thermodynamic analysis yields an entanglement entropy proportional to the horizon area, numerically matching the Bekenstein-Hawking entropy. All intermediate steps, including junction conditions, Kruskal extension, WKB modes, and UV regularization, are explicitly detailed. |
| title | Microscopic Origin of Bekenstein-Hawking Entropy in $(2+1)$ Gravity: A Thermo Field Dynamics Approach |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2602.22360 |