https://doi.org/10.1140/epjp/s13360-023-04624-8
Regular Article
A regular metric does not ensure the regularity of spacetime
1
Faculdade de Física, Programa de Pós-Graduação em Física, Universidade Federal do Pará, 66075-110, Belém, Pará, Brazil
2
Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do Pará Campus Universitário de Abaetetuba, 68440-000, Abaetetuba, Pará, Brazil
Received:
8
August
2023
Accepted:
20
October
2023
Published online:
3
November
2023
In this paper we try to clarify that a regular metric can generate a singular spacetime. Our work focuses on a static and spherically symmetric spacetime in which regularity exists when all components of the Riemann tensor are finite. There is work in the literature that assumes that the regularity of the metric is a sufficient condition to guarantee it. We study three regular metrics and show that they have singular spacetime. We also show that these metrics can be interpreted as solutions for black holes whose matter source is described by nonlinear electrodynamics. We analyze the geodesic equations and the Kretschmann scalar to verify the existence of the curvature singularity. Moreover, we use a change of the line element 
, which is a process of regularization of spacetime already known in the literature. We then recompute the geodesic equations and the Kretschmann scalar and show that all metrics now have regular spacetime. This process transforms them into black-bounce solutions, two of which are new. We have discussed the properties of the event horizon and the energy conditions for all models.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
