Isotropization of embedding Class I spacetime and anisotropic system generated by complexity factor in the framework of gravitational decoupling

Abstract

In this work, we present a hierarchical solution-generating technique employing the Minimum Gravitational Decoupling (MGD) Method and the generalized concept of Complexity as applied to Class I spacetime for bounded compact objects in classical general relativity. Starting off with an anisotropic seed solution described by Class I spacetime, we apply the MGD technique with the constraint that the effective anisotropy vanishes which leads to an isotropic model. In addition, we produce a second family of solutions in which the Complexity factor [Herrera (Phys Rev D 97:044010, 2018)] for the seed solution and its MGD counterpart are the same. We discuss the physical plausibility of both classes of solutions as candidates for physically realizable compact objects.

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]…”

Implications for vanishing complexity in dynamical spherically symmetric dissipative self-gravitating fluids

“…However, near the time of remnant formation where energy densities and pressures escalate to extreme measures, additional non-linear effects might arise, rendering the initial conditions and assumptions made in setting up the model of little relevance. In an effort to generate models, other physical constructs such as gravitational decoupling [7] and complexity factor analysis are now being considered. A definition of complexity from the statistical point of view was developed by López-Ruiz et al [8] and involves the interplay between entropy and information content.…”

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.…”