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.

arXiv comment23 pages, 4 figures

References in corpus (19)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Modified Gravity and Cosmology
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Constraints on dark energy from Chandra observations of the largest relaxed galaxy clusters
• The Third Data Release of the Sloan Digital Sky Survey
• Modified theories of Gravity: Why, How and What?
• Can the Universe Create Itself?
• A new time-machine model with compact vacuum core
• Ricci inverse gravity wormholes
• Ricci-inverse gravity: a novel alternative gravity, its flaws, and how to cure them
• A Self-Consistent Vacuum for Misner Space and the Chronology Protection Conjecture
• Ricci Inverse Anisotropic Stellar Structures
• Study of Compact Stars in $\mathcal{R}+\alpha \mathcal{A}$ Gravity
• Can we bypass no-go theorem for Ricci-inverse Gravity?
• Time Machines Constructed from Anti-de Sitter Space
• A type N radiation field solution with $\Lambda <0$ in a curved space-time and closed time-like curves
• Cosmological constant Petrov type-N space-time in Ricci-inverse gravity

Cited by in corpus (3)

• Quasinormal Modes and GUP-Corrected Hawking Radiation of BTZ Black Holes within Modified Gravity Frameworks
• Stationary BTZ space-time in Ricci-Inverse and $f(\mathcal{R})$ gravity theories
• Cylindrical black hole solutions in $f(\mathcal{R})$ and $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ modified gravity