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) and e^{-lambda }=mu +beta ,f(r), where beta 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} and the mimic constraint for the density {rho (r)=theta _0^0} (Ovalle in Phys Lett B 788:213, 2019). The compact star models have been constructed by taking M_0/R=0.2 for two different non-zero values of beta . 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 curve is also presented to support our model for describing a realistic compact object such as neutron stars.
Highlights
IntroductionAfter the splitting of Ti j , we solve Einstein’s equation for each of the above components
Ti j = {Ti j, θinj }. (1)After the splitting of Ti j, we solve Einstein’s equation for each of the above components
Based on the above discussion we can say that the minimal geometric deformation decoupling approach is a very powerful technique to discover solutions of Einstein’s equation for the self-gravitating stellar objects. Ovalle and his collaborators proposed that this MGD approach has some limitations as it fails to explain the existence of a stable black hole with a welldefined horizon because of the transformation undergone along only the radial metric component and temporal metric component is unchanged. This MGD was extended by deforming of both metric functions, and obtained modified Schwarzschild geometry, a new solution that describes the brane-world star [6], and derived the corrections to the gravitational wave radiation which is emitted by SU(N) EMGD dark glueball stars mergers [66]
Summary
After the splitting of Ti j , we solve Einstein’s equation for each of the above components. Ovalle and his collaborators proposed that this MGD approach has some limitations as it fails to explain the existence of a stable black hole with a welldefined horizon because of the transformation undergone along only the radial metric component and temporal metric component is unchanged In this regard, this MGD was extended by deforming of both metric functions, and obtained modified Schwarzschild geometry, a new solution that describes the brane-world star [6], and derived the corrections to the gravitational wave radiation which is emitted by SU(N) EMGD dark glueball stars mergers [66].
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