https://doi.org/10.1140/epjc/s10052-022-10108-3
Regular Article - Theoretical Physics
Testing generalized spacetimes for black holes using the Hod function representation of the hoop conjecture
1
Zel’dovich International Center for Astrophysics, M. Akmullah Bashkir State Pedagogical University, 3A, October Revolution Street, 450008, Ufa, RB, Russia
2
Department of Physics and Astronomy, Bashkir State University, 47A, Lenin Street, 453103, Sterlitamak, RB, Russia
3
Salavat Industrial College, 27, Matrosova Boulevard, 453259, Salavat, RB, Russia
Received:
6
January
2022
Accepted:
5
February
2022
Published online:
9
March
2022
The hoop conjecture, due to Thorne, is a fundamental aspect of black holes in classical general relativity. Recently, generalized classes of regular spherically symmetric static black holes with arbitrary exponents coupled to nonlinear electrodynamics have been constructed in the literature. The conjecture in those spacetimes could be violated if only the asymptotic mass is used. To avoid such violations, Hod earlier suggested the appropriate mass function and stated the conjecture in terms of what we call the Hod function. The conjecture can then be applied to any given static spacetime to test whether or not it represents black holes. It is shown here that the conjecture is protected in the above constructed class of generalized spacetimes thus supporting them as black holes. However, it is argued that there are factors, including violation of the conjecture, that militate against the proposed new class of solutions to be qualifying as black holes. Finally, we exemplify that the Hod mass
in the conjecture is exactly the matter counterpart of the Misner–Sharp geometrical quasilocal mass
of general relativity. Thus any conclusion based on Hod function is strictly a conclusion of general relativity.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3