Non-singular solution for anisotropic model by gravitational decoupling in the framework of complete geometric deformation (CGD)

Abstract

We presented a non-singular solution of Einstein’s field equations using gravitational decoupling by means of complete geometric deformation (CGD) in the anisotropic domain for compact star models. In this approach both the gravitational potentials are deformed as $$ \nu =\xi +\beta \,h(r)$$ν=ξ+βh(r) and $$ e^{-\lambda }=\mu +\beta \,f(r)$$e-λ=μ+βf(r), where $$\beta $$β is a coupling constant. Then we solve more complex field equations under above transformations by using a particular form of deformation function h(r) for two different cases namely the mimic constraint for the pressure $$\{p(r)=\theta ^1_1\}$${p(r)=θ11} and the mimic constraint for the density $$\{\rho (r)=\theta _0^0\}$${ρ(r)=θ00} (Ovalle in Phys Lett B 788:213, 2019). The compact star models have been constructed by taking $$M_0/R=0.2$$M0/R=0.2 for two different non-zero values of $$\beta $$β. Moreover, the boundary conditions are also performed for the said complete geometric deformation in the presence of anisotropic matter distribution. We also find pressure, density, anisotropy and causality conditions that are physically acceptable throughout the model. The $$M-R$$M-R curve is also presented to support our model for describing a realistic compact object such as neutron stars.

Role of gravitational decoupling on isotropization and complexity of self-gravitating system under complete geometric deformation approach

“…Due to this, we need only two extra conditions in order to close the system. There are many ways to solve the equation despite the appearance of the new degree of freedom h(r ) in the θ -sector, such as implementing the mimick approach with a particular form of h(r ), or using the EoS approach together with the mimick approach [19][20][21] to solve the -sector. On the other hand, it must be noted that the hydrostatic balance gets severely modified because of the deformation.…”

Spherically symmetric anisotropic charged solution under complete geometric deformation approach

“…So while working with EGD, it is very important to check the hydrostatic balance to find out the model is acceptable realistically or not. In light of EGD, some recent research work can be found in references [75,76].…”

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.…”