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

H. Nazar,G. Abbas

doi:10.1140/epjc/s10052-018-5973-z

H. Nazar, G. Abbas

Open Access

https://doi.org/10.1140/epjc/s10052-018-5973-z

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Abstract

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.

Highlights

Among the various definitions of complexity that have been planed up until now, a large portion of them depend on ideas, for example information and entropy, and depend on the natural thought that complexity should, somehow, amount a fundamental property showing the models, existing in the interior framework
The concept of complexity factor for the static anisotropic gravitating has been present by Herrera [1]
We have found that in the frame of f (R) gravity, the definition of complexity based on orthogonal splitting of the curvature tensor

Summary

Introduction

Among the various definitions of complexity that have been planed up until now, a large portion of them depend on ideas, for example information and entropy, and depend on the natural thought that complexity should, somehow, amount a fundamental property showing the models, existing in the interior framework. The symmetry of paper trails: in section, we have established the geometry of the gravitating anisotropic fluid source, variables related to the spherically symmetric static interior region, the modified Einstein field equations in f (R) background and useful settlements used thoroughly in this paper. The last section includes the summary of the work In this connection to present the physical significance of the gravitating source inside the celestial object formed by perfect fluid distribution and described with related variables under f (R) formalism. −gαβ ∇α∇α F(R) , is the effective energy–momentum tensor of the self-gravitating source, bounded by interior region configuration inside the interstellar model with f (R) modified theory of gravity.

The Riemann curvature and Weyl curvature tensor

The formulation of Tolman mass and the mass function

The orthogonal splitting of the curvature tensor

Matter distribution with disappearing complexity factor

Conclusions