The non-orientable spacetime of the eternal black hole

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Bibliographic Details
Main Author:	Racorean, Ovidiu
Format:	Preprint
Published:	2025
Subjects:	General Relativity and Quantum Cosmology
Online Access:	Acceder al recurso
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_version_	1866912546294857728
author	Racorean, Ovidiu
author_facet	Racorean, Ovidiu
contents	We derive the metric of the BTZ black hole for the special case of interchanging the characteristics of space and time coordinates. We maximally extend the geometry of this interior solution and show that the line element is similar to its exterior solution counterpart. Thus, we assign the thermofield double state dual to this interior geometric construction. As a result, we have two independent thermofield double states corresponding to the BTZ metric: one dual to the exterior solution and one dual to the interior solution. In this scenario, considering both thermofield double states as dual to the full BTZ black hole, we evaluate the partition function of the bulk. The partition function represents a non-orientable spacetime. Additionally, we derive a thermofield double-like state that connects in the gravity dual the regions of spacetime with opposite orientations of space and time.
format	Preprint
id	arxiv_https___arxiv_org_abs_2508_15005
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	The non-orientable spacetime of the eternal black hole Racorean, Ovidiu General Relativity and Quantum Cosmology We derive the metric of the BTZ black hole for the special case of interchanging the characteristics of space and time coordinates. We maximally extend the geometry of this interior solution and show that the line element is similar to its exterior solution counterpart. Thus, we assign the thermofield double state dual to this interior geometric construction. As a result, we have two independent thermofield double states corresponding to the BTZ metric: one dual to the exterior solution and one dual to the interior solution. In this scenario, considering both thermofield double states as dual to the full BTZ black hole, we evaluate the partition function of the bulk. The partition function represents a non-orientable spacetime. Additionally, we derive a thermofield double-like state that connects in the gravity dual the regions of spacetime with opposite orientations of space and time.
title	The non-orientable spacetime of the eternal black hole
topic	General Relativity and Quantum Cosmology
url	https://arxiv.org/abs/2508.15005

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