Abstract
In the present paper, we discuss the role of gravitational decoupling to isotropize the anisotropic solution of Einstein’s field equations in the context of the complete geometric deformation (CGD) approach and its influence on the complexity factor introduced by Herrera (Phys Rev D 97:044010, 2018) in the static self-gravitating system. Moreover, we proposed a simple and effective technique as well to generate new solutions for self-gravitating objects via CGD approach by using two systems with the same complexity factor and vanishing complexity factor proposed by Casadio et al. (Eur Phys J C 79:826, 2019). The effect of decoupling constant and the compactness on the complexity factor have also been analyzed for the obtained solutions.
Highlights
It can be said, that fixing some value of the complexity factor for a specific scenario can act as an equation of state which may lead close approximation to Einstein’s field equations
We develop a method of isotropization by employing a mathematical tool using gravitational decoupling in the framework of a complete geometric deformation (CGD) approach to find the new isotropic solutions from a known spacetime geometry for the anisotropic matter distribution
We investigated two new gravitationally decoupled anisotropic solutions by imposing the condition of two systems with the same complexity factor as well as systems with zero complexity factor
Summary
That fixing some value of the complexity factor for a specific scenario (example: a system having vanishing complexity) can act as an equation of state which may lead close approximation to Einstein’s field equations For these equations, it is very difficult to obtain analytical solutions. In this scenario, a recent well-known tool called Gravitational Decoupling (GD) by means of the minimal geometric deformation (MGD) [17] and its extension known as complete geometric deformation [18] formalism works perfectly to convert the isotropic solutions into anisotropic domain or can be even used to obtain new solutions. The MGD was extended to deform both radial and temporal met-
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