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 $$ \nu =\xi +\beta \,h(r)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mi>ξ</mml:mi><mml:mo>+</mml:mo><mml:mi>β</mml:mi><mml:mspace/><mml:mi>h</mml:mi><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and $$ e^{-\lambda }=\mu +\beta \,f(r)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>λ</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mi>μ</mml:mi><mml:mo>+</mml:mo><mml:mi>β</mml:mi><mml:mspace/><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> , where $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> 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 $$\{p(r)=\theta ^1_1\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>{</mml:mo><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mi>θ</mml:mi><mml:mn>1</mml:mn><mml:mn>1</mml:mn></mml:msubsup><mml:mo>}</mml:mo></mml:mrow></mml:math> and the mimic constraint for the density $$\{\rho (r)=\theta _0^0\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>{</mml:mo><mml:mi>ρ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mi>θ</mml:mi><mml:mn>0</mml:mn><mml:mn>0</mml:mn></mml:msubsup><mml:mo>}</mml:mo></mml:mrow></mml:math> (Ovalle in Phys Lett B 788:213, 2019). The compact star models have been constructed by taking $$M_0/R=0.2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mn>0.2</mml:mn></mml:mrow></mml:math> for two different non-zero values of $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> . 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 $$M-R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:mo>-</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:math> curve is also presented to support our model for describing a realistic compact object such as neutron stars.

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