We investigate irregularity factors for a self-gravitating spherical star evolving in the presence of an imperfect fluid. We explore the gravitational field equations and the dynamical equations with the systematic construction in $f(R,T)$ gravity, where $T$ is the trace of the energy-momentum tensor. Furthermore, we analyze two well-known differential equations (which occupy principal importance in the exploration of causes of energy density inhomogeneities) with the help of the Weyl tensor and the conservation laws. The irregularity factors for a spherical star are examined for particular cases of dust and isotropic and anisotropic fluids in dissipative and nondissipative regimes in the framework of $f(R,T)$ gravity. It is found that, as the complexity of the matter with the anisotropic stresses increases, the inhomogeneity factor corresponds more closely to one of the structure scalars.

Causes of Irregular Energy Density in $f(R,T)$ Gravity

The aim of this paper is to perform stability analysis of anisotropic dissipative cylindrical collapsing model in $f(R,T,R_{\mu\nu} T^{\mu\nu})$ gravity. In this context, the modified version of hydrodynamical equation is explored by means of dynamical equations and radial perturbation scheme. We examined the role of adiabatic index, dissipation as well as the particular cosmological model on the onset of dynamical instability of the evolving cylindrical system that was initially in hydrostatic equilibrium with Newtonian and post Newtonian approximations. It is pointed out that extra curvature terms of $f(R,T,R_{\mu\nu}T^{\mu\mu\nu})$ gravity tends to increase the stability, while that heat radiations push the system to enter into unstable window. Further, our results reveal the significance of adiabatic index in the stability analysis of cylindrical celestial model.

https://iopscience.iop.org/article/10.1088/1361-6382/aa73b9/pdf

Stability analysis of stellar radiating filaments

The aim of this paper is to explore some physically viable aspects for the possible emergence of compact stars in f(G,T) theory of gravity with some particular models, where G and T are Gauss–Bonnet invariant and trace of stress–energy tensor, respectively. We present basic formalism of this modified theory in the presence of anisotropic source. We explore some realistic aspects using the energy conditions with physical parameters. Three distinct known star models namely, SAXJ1808.4−3658, Her X−1 and 4U1820−30, are used for this systematic investigation. The physical behavior of anisotropic stresses, energy density, energy conditions, measure of anisotropy and stability of compact stars are discussed through plots. We conclude that compactness at the core of a star model increases and energy conditions hold.

Role of f(G,T) gravity on the evolution of relativistic stars

In a recent paper, Herrera (Phys Rev D 97:044010, 2018) have proposed a new definition of complexity for static self-gravitating fluid in general relativity. In the present article, we implement this definition of complexity for static self-gravitating fluid to case of f(R) gravity. Here, we found that in the frame of f(R) gravity the definition of complexity proposed by Herrera, entirely based on the quantity known as complexity factor which appears in the orthogonal splitting of the curvature tensor. It has been observed that fluid spheres possessing homogenous energy density profile and isotropic pressure are capable to diminish their the complexity factor. We are interested to see the effects of f(R) term on complexity factor of the self-gravitating object. The gravitating source with inhomogeneous energy density and anisotropic pressure have maximum value of complexity. Further, such fluids may have zero complexity factor if the effects of inhomogeneity in energy density and anisotropic pressure cancel the effects of each other in the presence of f(R) dark source term. Also, we have found some interior exact solutions of modified f(R) field equations satisfying complexity criterium and some applications of this newly concept to the study of structure of compact objects are discussed in detail. It is interesting to note that previous results about the complexity for static self-gravitating fluid in general relativity can be recovered from our analysis if $$f(R)=R$$
 , which general relativistic limit of f(R) gravity.

/pdf/complexity-factor-for-static-anisotropic-self-gravitating-3k81hmg2j7.pdf

Complexity factor for static anisotropic self-gravitating source in f( R) gravity

A previously found definition of complexity for spherically symmetric fluid distributions [1], is extended to axially symmetric static sources. In this case there are three different complexity factors, defined in terms of three structure scalars obtained from the orthogonal splitting of the Riemann tensor. All these three factors vanish, for what we consider the simplest fluid distribution, i.e a fluid spheroid with isotropic pressure and homogeneous energy density. However, as in the spherically symmetric case, they can also vanish for a variety of configurations, provided the energy density inhomogeneity terms cancel the pressure anisotropic ones in the expressions for the complexity factors. Some exact analytical solutions of this type are found and analyzed. At the light of the obtained results, some conclusions about the correlation (the lack of it) between symmetry and complexity, are put forward.

Complexity factors for axially symmetric static sources

The full set of equations governing the structure and the evolution of self--gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, is written down in terms of scalar quantities obtained from the orthogonal splitting of the Riemann tensor (structure scalars), in the context of general relativity. These scalars which have been shown previously (in the spherically symmetric case) to be related to fundamental properties of the fluid distribution, such as: energy density, energy density inhomogeneity, local anisotropy of pressure, dissipative flux, active gravitational mass etc, are shown here to play also a very important role in the dynamics of cylindrically symmetric fluids. It is also shown that in the static case, all possible solutions to Einstein equations may be expressed explicitly through three of these scalars.

L. Herrera

Papers

Cylindrically Symmetric Relativistic Fluids: A Study Based on Structure Scalars