$f(\mathcal{G},T_{\alpha \beta }{T}^{\alpha \beta })$ Theory and Complex Cosmological Structure

Abstract

The basic objective of this investigation is to explore the impact of a novel gravitational modification, specifically, the $f(\mathcal{G},{\mathbf{T}}^2)$ (where ${\mathbf{T}}^2\equiv T_{\alpha \beta }{T}^{\alpha \beta }$, $T^{\alpha \beta }$ denotes the stress-energy tensor) model of gravitation, upon the complexity of time-dependent dissipative as well as non-dissipative spherically symmetric celestial structures. To find the complexity factor $({\mathbb{C}}_{\mathbf{F}})$ from the generic version of the structural variables, we performed Herrera's scheme for the orthogonal cracking of Riemann tensor. In this endeavor, we are mainly concerned with the issue of relativistic gravitational collapse of the dynamically relativistic spheres fulfilling the presumption of minimal ${\mathbb{C}}_{\mathbf{F}}$. The incorporation of a less restrictive condition termed as quasi-homologous $({\mathbb{Q}}_{\mathbf{H}})$ condition together with the zero ${\mathbb{C}}_{\mathbf{F}}$, allows us to formulate a range of exact solutions for a particular choice of $f(\mathcal{G},{\mathbf{T}}^2)$ model. We find that some of the given exact solutions relax the Darmois junction conditions and describe thin shells by satisfying the Israel conditions, while some exhibit voids by fulfilling the Darmois constraints on both boundary surfaces. Eventually, few expected applications of the provided solutions in the era of modern cosmology are debated.

arXiv commentRevision submitted to Physics of the Dark Universe

References in corpus (53)

• f(R) Theories Of Gravity
• f(R) theories
• f(R,T) gravity
• Modified Gauss-Bonnet theory as gravitational alternative for dark energy
• Disappearing cosmological constant in f(R) gravity
• A Statistical Measure of Complexity
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Conditions for the cosmological viability of f(R) dark energy models
• Finite-time future singularities in modified Gauss-Bonnet and $\mathcal{F}(R,G)$ gravity and singularity avoidance
• Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction
• Construction of cosmologically viable f(G) gravity models
• Spherically symmetric dissipative anisotropic fluids: A general study
• Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday
• New definition of complexity for self-gravitating fluid distributions: The spherically symmetric, static case
• Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor
• Features of the Extension of a Statistical Measure of Complexity to Continuous Systems
• Causes of Irregular Energy Density in $f(R,T)$ Gravity
• From inflation to dark energy in the non-minimal modified gravity
• Stability of the isotropic pressure condition
• Definition of complexity for dynamical spherically symmetric dissipative self-gravitating fluid distributions
• Energy-Momentum Squared Gravity
• Tendency to Maximum Complexity in a Non-Equilibrium Isolated System
• Anisotropic Compact stars in the Buchdahl model: A comprehensive study
• $f(R,T_{\mu \nu }{T}^{\mu \nu })$ gravity and Cardassian-like expansion as one of its consequences
• Shearing Expansion-free Spherical Anisotropic Fluid Evolution
• String-Inspired Higher-Curvature Terms and the Randall-Sundrum Scenario
• Cosmological Models in Energy-Momentum-Squared Gravity
• On the stability of the shear-free condition
• Non-exotic matter wormholes in a trace of the energy-momentum tensor squared gravity
• Anisotropic compact stars in $f(R)$ gravity
• On the $\Lambda$CDM Universe in $f(G)$ gravity
• Statistical complexity, Fisher-Shannon information, and Bohr orbits in the H-atom
• Cosmological Constraints on $f(G)$ Dark Energy Models
• Compact stars in Energy-Momentum Squared Gravity
• Complexity and white-dwarf structure
• Quasi-homologous evolution of self-gravitating systems with vanishing complexity factor
• Can higher curvature corrections cure the singularity problem in f(R) gravity?
• Gauss-Bonnet Gravitational Baryogenesis
• Dynamical system analysis of generalized energy-momentum-squared gravity
• Complexity and neutron stars structure
• Expansion-Free Evolving Spheres Must Have Inhomogeneous Energy Density Distributions
• Existence of Compact Structures in $f(R,T)$ Gravity
• Constraint on energy-momentum squared gravity from neutron stars and its cosmological implications
• On the Role of $f(G,T)$ Terms in Structure Scalars
• Screening $\Lambda$ in a new modified gravity model
• Cavity evolution in relativistic self-gravitating fluids
• Connecting early and late universe by $f(R)$ gravity
• Cosmological implications of scale-independent energy-momentum squared gravity: Pseudo nonminimal interactions in dark matter and relativistic relics
• Evolution of Compact Stars and Dark Dynamical Variables
• Late time cosmological approach in mimetic $f(R,T)$ gravity
• Temporally Varying Universal Gravitational "Constant" and Speed of Light in Energy Momentum Squared Gravity
• Gauss-Bonnet Cosmology Unifying Late and Early-time Acceleration Eras with Intermediate Eras
• Role of Structure Scalars on the evolution of Compact Objects in Palatini $f(R)$ Gravity

Cited by in corpus (12)

• Interpretation of complexity for spherically symmetric fluid composition within the context of modified gravity theory
• Orthogonal splitting of the Riemann curvature tensor and its implications in modeling compact stellar structures
• Role of Complexity on the Minimal Deformation of Black Holes
• Imprints of dark matter on the structural properties of minimally deformed compact stars
• Big Bang Nucleosynthesis constraints on $f(T,T_G)$ gravity
• Complexity factor of spherically anisotropic polytropes from gravitational decoupling
• Junction conditions in gravity theories with extra scalar degrees of freedom
• Non-Singular Bouncing Model in Energy Momentum Squared Gravity
• Possible Existence of Ghost Stars in the context of Electromagnetic Field
• Completely Deformed Complexity-free Anisotropic Fluid Sphere
• Stability of Relativistic Spheres Powered by Energy Profile in Einstein Gauss-Bonnet Gravity
• Exact $(1+3+6)$-dimensional cosmological-type solutions in gravitational model with Yang-Mills field, Gauss-Bonnet term and $\Lambda$-term