https://doi.org/10.1140/epjp/s13360-025-07184-1
Regular Article
Investigating equilibrium and instability in anisotropic spacetimes through complexity to cracking
1
Institute of Mathematics, University of the Punjab, 54590, Lahore, Pakistan
2
Department of Physics and Astronomy, University of Calgary, Calgary, AB, Canada
3
Tashkent International University of Education, Imom Bukhoriy 6, 100207, Tashkent, Uzbekistan
4
University of Tashkent for Applied Sciences, Str. Gavhar 1, 100149, Tashkent, Uzbekistan
5
Tashkent State Technical University, 100095, Tashkent, Uzbekistan
6
National University of Uzbekistan, 100174, Tashkent, Uzbekistan
7
Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, 1096, Baku, Azerbaijan
a
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Received:
6
August
2025
Accepted:
7
December
2025
Published online:
23
December
2025
Abstract
This article explores how cracking and complexity affect the stability of certain objects in space, using the Rastall theory. The goal is to understand how minor adjustments or perturbations impact the stability of compact objects. This work examines the field equations and the generalized non-conservation equation in Rastall theory, assuming a non-static spacetime geometry with an anisotropic fluid. We further examined the relationship between the Rastall parameter and energy density as well as the mass of a gravitationally bound system. The complex nature of fluid structure and its evolution is examined by considering two different modes, homologous and quasi-homologous regimes. The complexity of self-gravitating spheres is calculated using the scalar function (
), derived from the covariant splitting of the Riemann tensor. Then, within the context of Rastall theory, the idea of cracking is examined in the case of several models. The analysis shows that cracking occurs only in anisotropic objects, regardless of the complexity factor within the Rastall theory context. Additionally, it is demonstrated that departing from equilibrium in either homologous or quasi-homologous regimes prevents cracking. The results indicate that considering a zero complexity factor in different cases impacts cracking, which only occurs in dissipative isotropic and geodesic cases.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
