Complexity factors for static anisotropic axially symmetric fluid distributions in f(R) gravity

Abstract

In this paper, we have analyzed the complexity factor for the most general axially symmetric static anisotropic fluid distributions in context of [Formula: see text] theory of gravity. For this purpose, we have studied three distinct complexity factors that are organized in terms of three scalar variables (structure scalars) comes from the orthogonal splitting of the curvature tensor. The vanishing of all complexity factors condition for what we choose the simplest fluid distribution that in which system having energy density is homogeneous with isotropic pressure. Although, it has been found that the complexity factors condition can also vanish when inhomogeneous energy density and anisotropy of the pressure cancel each other. Next, we express a class of exact solutions and their graphical analysis as compatible to our models that satisfies the vanishing condition of complexity factors. Finally, it is worth mentioning that these results can reproduce the results of General theory of Relativity under some constraints.

Traversable wormholes with like-Casimir complexity supported with arbitrarily small amount of exotic matter

“…Other possibilities could be either to supply an equation of state and one of the metric functions or to provide one of the metric functions and a metric constraint. In this work we propose an alternative route consisting in setting of a suitable metric and a specific complexity factor introduced in [26] which has been broadly used as a complementary condition to solve the Einstein equations in different contexts [27][28][29][30][31][32][33]. The reason of introducing the complexity factor is twofold.…”

Quasi-homologous evolution of self-gravitating systems with vanishing complexity factor

“…The presented arguments in [2] strongly suggested that the homologous condition seemed to be the most suitable to describe the simplest mode of evolution. The applications of this concept including systems with different kind of symmetry and/or other theories of gravity, may be found in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and references therein.…”

Study of generalized cylindrical polytropes with complexity factor

“…Different equations of state are playing an important role to describe the two very fundamental aspect of universe, dark energy and dark matter. Babichev et al [35] used a form of linear equation of state, called generalized linear equation of state with perfect fluid distribution to describe the different scenarios for dark energy. Mukhopadhyay et al [18] discussed the real nature of dark energy through the parameter of PEoS specially in non-dust situation.…”

“…Herrera [31] used orthogonal splitting of Riemann tensor into structure scalars for a self gravitating system to present a new concept of complexity factor (CF). Abbas and Nazar [32][33][34][35] carried out this concept of vanishing CF for self gravitating object in the context of modify gravity f (R) and expressed the physical behavior of f (R) model for some compact objects in spherically static, dynamical and axially symmetry . Sharif and Iqra [36,37] implemented the CF on cylindrical system and discussed the electromagnetic effect on this system.…”