An EGD model in the background of embedding class I space–time

Abstract

This work is devoted to the study of relativistic anisotropic compact objects. To obtain this class of solutions of the Einstein field equations, we have developed a general scheme to generate the metric of the space–time describing the interior of the compact structure. This approach is based on the class I space–time and the extended gravitational decoupling by means of an extended geometric deformation (EGD). The class I condition provides a differential equation relating both metric potential $$\nu $$ ν and $$\lambda $$ λ , whilst the EGD translates the metric potentials to $$ \nu =\xi +\beta \,h(r)$$ ν = ξ + β h ( r ) and $$ \lambda =-\ln [\mu +\beta \,f(r)]$$ λ = - ln [ μ + β f ( r ) ] , where h(r) and f(r) are the deformation functions and $$\beta $$ β a dimensionless constant. In this case the pair $$\{\xi ,\mu \}$$ { ξ , μ } represents the seed solution satisfying the class I condition without any deformation. Once the deformed metric potentials are inserted into the class I, the main task is to obtain h(r) or f(r). So, in this case a particular ansatz for h(r) is considered in conjunction with $$\beta =0.5$$ β = 0.5 to get f(r). In order to check feasibility of our model, we have performed a thoroughly physical, mathematical and graphical analysis.

Class I polytropes for anisotropic matter

“…Finally, introducing (42) in (35) we arrive to the class I generalized Lane-Emden equation for γ = 1 (isothermal case),…”

Gravitational decoupling of generalized Horndeski hybrid stars

“…The gravitational decoupling was also used to study gravity coupled to hidden gauge fields [30] and to derive new physical features of superfluid stars [31]. Other models involving the gravitational decoupling have been developed [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], with relevant applications to recently observed anisotropic stellar configurations [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]. Also, the quantum entanglement entropy of anisotropic gravitational decoupled black holes revealed important directions towards placing the gravitational decoupling method in gauge/gravity duality [68,69].…”

Exploring Physical Properties of Gravitationally Decoupled Anisotropic Solution in 5D Einstein‐Gauss‐Bonnet Gravity

“…The general framework for studying class I spacetimes within the context of the MGD and CGD approaches were provided by Maurya and his collaborators. [ 48–50 ] The MGD in axially symmetric systems and rotating black holes has been applied by Contreras et al. [ 43 ] as well as some other works on dark matter, black holes and Dirac stars in the context of MGD are obtained by the authors.…”