Influence of f(G) gravity on the complexity of relativistic self-gravitating fluids

In this paper, we extend the notion of complexity for the case of nonstatic self-gravitating spherically symmetric structures within the background of modified Gauss–Bonnet gravity (i.e. [Formula: see text] gravity), where [Formula: see text] denotes the Gauss–Bonnet scalar term. In this regard, we have formulated the equations of gravity as well as the relations for the mass function for anisotropic matter configuration. The Riemann curvature tensor is broken down orthogonally through Bel’s procedure to compose some modified scalar functions and formulate the complexity factor with the help of one of the scalar functions. The CF (i.e. complexity factor) comprehends specific physical variables of the fluid configuration including energy density inhomogeneity and anisotropic pressure along with [Formula: see text] degrees of freedom. Moreover, the impact of the dark source terms of [Formula: see text] gravity on the system is analyzed which revealed that the complexity of the fluid configuration is increased due to the modified terms.

Structure scalars and their evolution for massive objects in f(R) gravity

In this manuscript, the Riemann tensor is split orthogonally to get five scalar functions known as structure scalars which have significance to gain insight into the composition and structure of spherically symmetric self-gravitating objects. Certain stellar equations are then evaluated to gather information about physical characteristics of such astrophysical objects. These stellar equations are further written in terms of acquired structure scalars so that the basic properties such as pressure anisotropy and energy density inhomogeneity of the fluid under consideration can be explored. Also, we have explored few static spherically symmetric solutions to show significance of structure scalars in the background of f(R) gravity.

Influence of modification of gravity on the complexity factor of static spherical structures

ABSTRACT The aim of this paper is to generalize the definition of complexity for the static self-gravitating structure in f (R, T, Q) gravitational theory, where R is the Ricci scalar, T is the trace part of energy–momentum tensor, and Q ≡ RαβT αβ. In this context, we have considered locally anisotropic spherical matter distribution and calculated field equations and conservation laws. After the orthogonal splitting of the Riemann curvature tensor, we found the corresponding complexity factor with the help of structure scalars. It is seen that the system may have zero complexity factor if the effects of energy density inhomogeneity and pressure anisotropy cancel the effects of each other. All of our results reduce to general relativity on assuming f (R, T, Q) = R condition.

Complexity analysis of dynamical spherically-symmetric dissipative self-gravitating objects in modified gravity

In this paper, we have worked on the concept of complexity factor for nonstatic spherically-symmetric self-gravitating source filled with anisotropic fluid distribution in [Formula: see text] gravity theory. The definition of complexity for dynamical sources, proposed by Herrera, is examined in the framework of [Formula: see text] gravity. We intended to analyze the behavior of complexity factor in modified theory. For this, we defined the scalar functions through orthogonal splitting of Reimann tensor in [Formula: see text] gravity and worked out the structure scalars. We considered the structure scalar [Formula: see text] as a complexity factor to evaluate the complexity of the structure of dynamical system and also to analyze the complexity of the evolutionary patterns of the system under consideration. We took into account the homologous condition and homogeneous expansion condition in order to present the simplest mode of evolution, and found that homologous evolution is the simplest one. We considered both dissipative and nondissipative cases and found that shearing behavior of the fluid is not the same in both cases, however it remained geodesic in both cases. In the end, we established the results for the vanishing of the complexity factor. It has been found that zero complexity condition is satisfied if the energy density inhomogeneity and pressure anisotropy of the fluid configuration cancel each other.

Dynamics and stability of charged spherical star with tilted and non-tilted congruences

This paper investigates the dynamics of anisotropic viscous spherical star under the effects of electromagnetic field for a radially moving observer relative to the matter distribution, i.e. a tilted observer. We formulate relationship between tilted and non-tilted quantities using the Einstein–Maxwell field equations. The dynamical equations and equations for the Weyl tensor are constructed to examine the inhomogeneities in the fluid configuration. It is found that different factors like heat radiation, shear viscosity, electric charge and in particular congruence of the tilted observer, affect the energy density inhomogeneity of the spherical star. Finally, we study stability of the system with non-tilted frame in the presence of charge.

Electromagnetic effects on the inhomogeneity of planar symmetry

In this work, we aim to identify the effects of electromagnetic field on the energy density inhomogeneity in self-gravitating plane symmetric spacetime filled with imperfect matter in terms of dissipation and anisotropic pressure. We formulate the Einstein–Maxwell field equation, conservation laws, evolution equations for the Weyl tensor and the transport equation for diffusion approximation. Inhomogeneity factors are identified for some particular cases of non-dissipative and dissipative fluids. For non-dissipative case, we analyze the inhomogeneity factor for dust, isotropic and anisotropic matter distributions while dissipative matter distribution includes the inhomogeneity factor only for geodesic dust fluid. We conclude that electric charge increases the inhomogeneity in the energy density which is due to shear, anisotropy and dissipation.

Effects of some physical factors on the inhomogeneity in planar symmetry

This paper is devoted to identify some physical causes of energy density inhomogeneity and stability of self-gravitating relativistic fluids in plane symmetry such as Weyl tensor, local anisotropy, dissipative terms and their specific combination. We first develop a relationship between matter variables and the Weyl tensor and then formulate dynamical equations using Bianchi identities. For the non-dissipative dust fluid, we conclude that the system will remain homogeneous if and only if it is conformally flat which implies the shear-free condition. However, the converse is not true for the non-dissipative isotropic fluid. For non-dissipative anisotropic fluid, the inhomogeneity factor is identified to be one of the structure scalars. A particular case of geodesic with dissipation is also discussed.

Dissipative planar gravitational collapse in f(G) gravity

This paper is devoted to analyze the dynamics of plane symmetric gravitational collapse as well as energy density inhomogeneity in f(G) gravity. The field equations are constructed for dissipative isotropic source and Darmois junction conditions are used to discuss the process of collapse. We use Misner–Sharp mechanism to develop dynamical equation and couple it with transport equation to explore the impact of gravitational force on the collapsing rate. For constant f(G) model, we conclude that the rate of collapse slows down. Finally, we discuss the relationship between the Weyl tensor and physical quantities.