# Durgapal IV model in light of the minimal geometric deformation approach

• The present article is devoted to the study of local anisotropies effects on the Durgapal's fourth model in the context of gravitational decoupling via the Minimal Geometric Deformation approach. To do it, the most general equation of state relating the components of the $\theta$−sector is imposed to obtain the decoupler function $f(r)$. In addition, certain properties of the obtained solution are investigated, such as the behavior of the salient material content threading the stellar interior, causality and energy conditions, hydrostatic balance through modified Tolman−Oppenheimer−Volkoff conservation equation and stability mechanism against local anisotropies by means of adiabatic index, sound velocity of the pressure waves, convection factor and Harrison−Zeldovich−Novikov procedure, in order to check if the model is physically admissible or not. Regarding the stability analysis, it is found that the model presents unstable regions when the sound speed of the pressure waves and convection factor are used in distinction with what happens in the adiabatic index and Harrison−Zeldovich−Novikov case. To produce a more realistic picture the numerical data for some known compact objects was placed and different values of the parameter $\alpha$ were considered to compare with the GR case i.e, $\alpha=0$.

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Francisco Tello-Ortiz, Ángel Rincón, Piyali Bharz and Y. Gomez-Leyton. Durgapal IV model in light of the minimal geometric deformation approach[J]. Chinese Physics C.
Francisco Tello-Ortiz, Ángel Rincón, Piyali Bharz and Y. Gomez-Leyton. Durgapal IV model in light of the minimal geometric deformation approach[J]. Chinese Physics C.
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## Durgapal IV model in light of the minimal geometric deformation approach

• Departamento de Física, Facultad de ciencias básicas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile
• Instituto de Física, Pontificia Universidad Católica de Valparáso, Avenida Brasil 2950, Casilla 4059, Valparáso, Chile
• Department of Mathematics,Government General Degree College, Singur, Hooghly, West Bengal 712 409, India
• Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile

Abstract: The present article is devoted to the study of local anisotropies effects on the Durgapal's fourth model in the context of gravitational decoupling via the Minimal Geometric Deformation approach. To do it, the most general equation of state relating the components of the $\theta$−sector is imposed to obtain the decoupler function $f(r)$. In addition, certain properties of the obtained solution are investigated, such as the behavior of the salient material content threading the stellar interior, causality and energy conditions, hydrostatic balance through modified Tolman−Oppenheimer−Volkoff conservation equation and stability mechanism against local anisotropies by means of adiabatic index, sound velocity of the pressure waves, convection factor and Harrison−Zeldovich−Novikov procedure, in order to check if the model is physically admissible or not. Regarding the stability analysis, it is found that the model presents unstable regions when the sound speed of the pressure waves and convection factor are used in distinction with what happens in the adiabatic index and Harrison−Zeldovich−Novikov case. To produce a more realistic picture the numerical data for some known compact objects was placed and different values of the parameter $\alpha$ were considered to compare with the GR case i.e, $\alpha=0$.

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