Time-Machines Construct in $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ and $f(\mathcal{R})$ Modified Gravity Theories

Abstract

In this paper, our objective is to explore a time-machine space-time formulated in general relativity, as introduced by Li (Phys. Rev. D {\bf 59}, 084016 (1999)), within the context of modified gravity theories. We consider Ricci-inverse gravity of all Classes of models, {\it i.e.}, (i) Class-{\bf I}: $f(\mathcal{R},\mathcal{A})=(\mathcal{R}+\kappa {\mathcal{R}}^2+\beta \mathcal{A})$, (ii) Class-{\bf II}: $f(\mathcal{R},A^{\mu \nu }{A}_{\mu \nu })=(\mathcal{R}+\kappa {\mathcal{R}}^2+\gamma A^{\mu \nu }{A}_{\mu \nu })$ model, and (iii) Class-{\bf III}: $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })=(\mathcal{R}\kappa {\mathcal{R}}^2+\beta \mathcal{A}+\delta {\mathcal{A}}^2+\gamma A^{\mu \nu }{A}_{\mu \nu })$ model, where $A^{\mu \nu }$ is the anti-curvature tensor, the reciprocal of the Ricci tensor, $R_{\mu \nu }$, $\mathcal{A}=g_{\mu \nu }{A}^{\mu \nu }$ is its scalar, and $\beta ,\kappa ,\gamma ,\delta$ are the coupling constants. Moreover, we consider $f(\mathcal{R})$ modified gravity theory and investigate the same time-machine space-time. In fact, we show that Li time-machine space-time serve as valid solutions both in Ricci-inverse and $f(\mathcal{R})$ modified gravity theories. Thus, both theory allows the formation of closed time-like curves analogue to general relativity, thereby representing a possible time-machine model in these gravity theories theoretically.

23 pages, 4 figures

References in corpus (3)

• Modified theories of Gravity: Why, How and What?
• Ricci Inverse Anisotropic Stellar Structures
• Study of Compact Stars in $\mathcal{R}+\alpha \mathcal{A}$ Gravity