Eur. Phys. J. C (2024) 84: 968
https://doi.org/10.1140/epjc/s10052-024-13327-y

Regular Article - Theoretical Physics

Axially symmetric solutions in Ricci-inverse modified gravity

¹ Department of Physics, University of Science and Technology Meghalaya, Ri-Bhoi, 793101, Meghalaya, India
² Programa de Pós-Graduação em Física, Instituto de Física, Universidade Federal de Mato Grosso, Cuiabá, Brasil

^c alesandroferreira@fisica.ufmt.br

Received: 1 July 2024
Accepted: 3 September 2024
Published online: 27 September 2024

Abstract

We investigate a family of axial symmetry solution constructed in general relativity (GR) within the framework of Ricci-inverse (RI) gravity theory. In GR, these solutions admitted closed time-like curves at an instant of time from an initial spacelike hypersurface in a causally well-behaved manner, thus, violates the causality condition. Our aim is to examine these axial symmetry solutions within the context of Ricci-inverse gravity theory to determine whether closed time-like curves still appear in this new gravity theory. We consider two Classes of RI-gravity models: (i) Class-II models defined by a function $f=f(\mathcal{R},A^{\mu \nu }{A}_{\mu \nu })$ gravity and (ii) Class-III models defined by $f=f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$, where $A^{\mu \nu }$ is the anti-curvature tensor, $\mathcal{A}=g_{\mu \nu }{A}^{\mu \nu }$ as its scalar, and $R^{\mu \nu }$ is the Ricci tensor. We are able solved the modified field equations considering these axial symmetry solutions as background in RI-gravity with null radiation as the matter content and the cosmological constant. This confirms that the chosen family of axial symmetry solutions are valid solutions in RI-gravity theory and, consequently, closed time-like curves is still form, analogous to their formation in GR.