Orthogonal splitting of the Riemann curvature tensor and its implications in modeling compact stellar structures

Abstract

Although the interpretation of complexity in extended theories of gravity is available in the literature, its illustration in $f(R,L_m,\mathcal{T})$ theory is still ambiguous. The orthogonal decomposition of the Riemann tensor results in the emergence of complexity factor as recently proposed by Herrera [1]. We initiate the analysis by contemplating the interior spacetime as a static spherical anisotropic composition under the presence of charge. The modified field equations are derived along with the establishment of association between the curvature and conformal tensors that have significant relevance in evaluating complexity of the system. Furthermore, the generalized expressions for two different masses are calculated, and their link with conformal tensor is also analyzed. Moreover, we develop a particular relation between predetermined quantities and evaluate the complexity in terms of a certain scalar $Y_{TF}$. Several interior solutions admitting vanishing complexity are also determined. Interestingly, compact objects having anisotropic matter configuration along with the energy density inhomogeneity possess maximum complexity. It is concluded that the spherical distribution of matter might not manifest complexity or admitting minimal value of this factor in the framework of $f(R,L_m,\mathcal{T})$ theory due to the appearance of dark source terms.

36 pages, 1 figure

References in corpus (37)

• f(R,T) gravity
• Disappearing cosmological constant in f(R) gravity
• Extra force in $f(R)$ modified theories of gravity
• Conditions for the cosmological viability of f(R) dark energy models
• The Mass and Radius of the Neutron Star in 4U 1820-30
• Charged anisotropic models for quark stars
• General class of wormhole geometries in conformal Weyl gravity
• Statistical complexity, Fisher-Shannon information, and Bohr orbits in the H-atom
• On the way from matter-dominated era to dark energy universe
• Role of Tilted Congruence and $f(R)$ Gravity on Regular Compact Objects
• Complexity factors for axially symmetric static sources
• Quasi-homologous evolution of self-gravitating systems with vanishing complexity factor
• Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity
• Definition of Complexity Factor for Self-Gravitating Systems in Palatini $f(R)$ Gravity
• $f(\mathcal{G},T_{\alpha \beta }{T}^{\alpha \beta })$ Theory and Complex Cosmological Structure
• Existence of Non-singular Stellar Solutions within the context of Electromagnetic Field: A Comparison between Minimal and Non-minimal Gravity Models
• Complexity and neutron stars structure
• Complexity and Isotropization based Extended Models in the context of Electromagnetic Field: An Implication of Minimal Gravitational Decoupling
• Anisotropic compact stars in Karmarkar spacetime
• Conformal invariance of chiral edge theories
• Gravitational cracking and complexity in the framework of gravitational decoupling
• Connecting early and late universe by $f(R)$ gravity
• Hyperbolically symmetric static fluids: A general study
• To conserve, or not to conserve: A review of nonconservative theories of gravity
• Interpretation of complexity for spherically symmetric fluid composition within the context of modified gravity theory
• Late time cosmological approach in mimetic $f(R,T)$ gravity
• A comparative study between EGB gravity and GTR by modelling compact stars
• Effect of Extended Gravitational Decoupling on Isotropization and Complexity in f(\mathbb{R},\mathbb{T}) Theory
• Effects of Charge and Gravitational Decoupling on Complexity and Isotropization of Anisotropic Models
• Non-singular anisotropic solutions for strange star model in $f(\mathcal{R},\mathcal{T},{\mathcal{R}}_{\zeta \gamma }{\mathcal{T}}^{\zeta \gamma })$ gravity theory
• Applicability of Modified Gauss-Bonnet Gravity Models on the Existence of Stellar Structures
• Class I polytropes for anisotropic matter
• An analytical anisotropic compact stellar model of embedding class I
• Estimating the Role of Bag Constant and Modified Theory on Anisotropic Stellar Models
• Complexity of Dynamical Dissipative Cylindrical System in Non-minimally Coupled Theory
• Thermodynamics and Perturbative Analysis of Some Newly Developed $\mathcal{F}(R,L_m,T)$ Theories Under the Scenario of Conserved Energy-momentum Tensor
• Kerr Initial data

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