Role of Complexity on Self‐gravitating Compact Star by Gravitational Decoupling

Abstract

In this paper, we study novel classes of solutions characterizing the role of complexity on static and spherically symmetric self‐gravitating systems proposed by L. Herrera (Phys Rev D 97: 044010, 2018) in the gravitational decoupling background. We start by considering the minimal geometric deformation approach as a ground‐breaking tool for generating new physically viable models for anisotropic matter distributions by exploiting the Buchdahl and Tolman models. In both models, all solutions show similar results with a slight change in their magnitude for a non‐vanishing complexity factor i.e., , where β is a decoupling constant. However, under vanishing complexity factor i.e., , the minimally deformed anisotropic Buchdahl model yielded a constant density isotropic fluid distribution and anisotropic matter distribution becomes an isotropic fluid matter distribution without invoking any isotropy requirement. On the other hand, Tolman model possesses an increasing pressure when the complexity factor vanishes. Furthermore, we also extend our findings by calculating the mass‐complexity factor relationship for both presented models, revealing that the mass is larger for small values of the decoupling constant β and the complexity factor .

An anisotropic extension of Heintzmann IIa solution with vanishing complexity factor

“…This framework permit us use a known isotropic solution as a seed and extra condition (examples of such conditions are the mimic constrain for the pressure or energy density, barotropic equation of state, regularity of anisotropic pressure, complexity factor, among other) in order to close the entire system of EFE (for the implementation of this framework with the use of several seed solutions see Refs. [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]). Even this framework has been used widely in several scenarios such as 2 + 1 space-times [50][51][52][53][54][55], higher dimensions [56,57], asymptotically (A-)dS space-times [58], for axially symmetric systems and rotating black holes [59], hairy black holes [60][61][62], Cosmology [63,64], solutions in the background of Reissner-Nordström space-time [65][66][67], modified gravity theories [68][69][70][71][72][73][74][75]…”

A simple protocol to construct solutions with vanishing complexity by Gravitational Decoupling

“…As we shall see later, although the radial deformation can be obtained independently after imposing some suitable equation of state, obtaining the temporal deformation is not straightforward in general. In this work we demonstrate that the complexity factor introduced in [64] (for recent developments see [65][66][67][68][69][70][71][72][73][74], for example) can be used to obtain a constraint on the metric functions which allow to obtain the temporal defora e-mails: econtreras@usfq.edu.ec ; ernesto.contreras@gmail.com (corresponding author) b e-mail: zdenek.stuchlik@physics.slu.cz mation analytically. The interest on the complexity factor has increase in recent years given that it provides useful information about how "complex" is a system in comparison with that supported by a homogeneous and isotropic fluid satisfying the so-called vanishing complexity condition.…”

A simple protocol for anisotropic generalization of Finch–Skea model by gravitational decoupling satisfying vanishing complexity factor condition

“…They came to the conclusion that Tolman's mass in this scenario reflects negative nature. Furthermore, many researchers have effectively employed this complexity approach not only in GR [91][92][93][94][95], but also in the analysis of findings for various geometries in the context of modified theory of gravity [96][97][98].…”