Definition of complexity factor for self-gravitating systems in Palatini f(R) gravity

Abstract

The aim of this paper is to explore the complexity factor for those self-gravitating relativistic spheres whose evolution proceeds non- dynamically. We are adopting the definition of CF mentioned in (Herrera 2018 Phys. Rev. D 97, 044010), modifying it to the static spherically symmetric case, within the framework of a modified gravity theory (the Palatini f(R) theory). In this respect, we have considered radial dependent anisotropic matter content coupled with spherical geometry and determined the complexity factor involved in the patterns of radial evolution. We shall explore the field and a well-known Tolman-Oppenheimer-Volkoff equations. After introducing structure scalars from the orthogonal decomposition of the Riemann tensor, we shall calculate complexity factor. An exact analytical model is presented by considering firstly ansatz provided by Gokhroo and Mehra. The role of matter variables and f(R) terms are analyzed in the structure formation as well as their evolution through a complexity factor.

Role of f(G) gravity in the study of non-static complex systems

“…In terms of structure scalars, Herrera et al [25] proposed all possible solutions of Einstein field equations for static spherically symmetric cases. Yousaf and Bhatti [26], Yousaf [13,27,28] also Yousaf et al [29] explored these results in modified theories for different cosmos models. For static fluid distributions, the complexity factor is described [10] and also it is defined for dynamical self-gravitating configurations [1].…”

“…In terms of general relativity, a new definition of complexity for various self-gravitating fluids [1,10,11] was established a few years ago. The conception of this new work of complexity is extended to modified theories [12][13][14][15][16][17][18][19]. According to a new definition of complexity, a fluid configuration that is spherically symmetric and static is based on the idea that minimal complex systems resemble the isotropic and homogeneous fluid distribution.…”

Hyperbolically symmetric sources in Palatini f(R) gravity

“…So, we may use another metric tensor notation i.e. h πν = f R g πν from where cosmic attributes of vacuum space in the context of f (R) theory can be observed [32]. Mathematically, the following relation may be established between this new form of metric tensor and the connection…”

Spatially Hyperbolic Gravitating Sources in Λ-Dominated Era

“…This single tool deals with different aspects of the system, providing a lot of information about the evolution of the system, e.g., shear and expansion evolution, inhomogeneity, complexity, etc., can be dealt with through these structure scalars [34][35][36]. Yousaf and his collaborators [16,[37][38][39][40][41] computed the modified version of these scalars by invoking extra curvature terms and described their influences in understanding the evolutionary mechanisms of adiabatic and non-adiabatic relativistic structures. Herrera [42] introduced a new concept of complexity factor in terms of one of these scalars for the static anisotropic spherical objects.…”