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

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.

Decoupling gravitational sources by MGD approach in Rastall gravity

“…Next, following the discussion in section V the constant parameters, namely A, B and C defining the interior solution can be obtained from Eqs. (50) and (64) leading to…”

“…As before, the parameters A, B and C are obtained from the junction conditions. However, the imposition of constraint (78) slightly changes the information obtained from condition (50). Now from (50) one gets an expression for constant C in terms of the radius R, the constant A, and the free parameters α and λ.…”

“…In this respect, the well known Tolman solutions have been extended into the Rastall gravity arena [49] in order to contrast the behavior of the main salient features with the corresponding GR ones. Furthermore, to reinforce the study of stellar interiors in the Rastall scenario an anisotropic model in the background of Krori-Barua (KB) space-time was done in [50] (in [51] the same authors considered KB space-time supplemented by an equation of state, specifically a quintessence model) and an isotropic compact object using conformal Killing vector technique was reported in [52]. Regarding the strong gravitational regime, remarkable solutions of black holes were presented in [53,54].…”

Complexity of dynamical sphere in self-interacting Brans–Dicke gravity

“…In [31], Y T F was chosen as the complexity factor of the static sphere because it incorporated the essential features of the system and determined their effects on Tolman mass (or active gravitational mass). Equation (34) indicates that Y T F contains the contribution of the significant factors which induce complexity in the current setup. Therefore, we proceed by assuming that the scalar Y T F is the best fit for the complexity factor.…”

“…Recently, the complexity of different geometries has also been explored by employing Herrera's definition and it was shown that complexity of the self-gravitating structures increases in the presence of a massive scalar field [31][32][33]. The concept of complexity has been analyzed in other modified theories as well [34] In this paper, we derive the complexity factor for a dynamical dissipative sphere by considering its pattern of evolution in the background of SBD theory. The paper is organized as follows.…”