Self-gravitating anisotropic model in general relativity under modified Van der Waals equation of state: a stable configuration

Abstract

Abstract The purpose of this paper consists in presenting models of compact stars described by a new class of exact solutions to the field equations, in the context of general relativity, for a fluid configuration which is locally anisotropic in the pressure. With current sensitivities, we considered a non-linear form of modified Van der Waals equation of state viz., $$p_{r}=\alpha \rho ^{2} +\frac{\beta \rho }{1+\gamma \rho }$$ p r = α ρ 2 + β ρ 1 + γ ρ , as well as a gravitational potential Z(x) as a generating function by exploiting an anisotropic source of matter which served as a basis for generating the confined compact stars. The exact solutions are formed by correlating an interior space-time geometry to an exterior Schwarzschild vacuum. Then, we analyze the physical viability of the model generated and compare it with observational data of some heavy pulsars coming from the Neutron Star Interior Composition Explorer. The model satisfies all the required pivotal physical and mathematical properties in the compact structures study, offering empirical evidence in support of the evolution of realistic stellar configurations. It is shown to be regular, viable, and stable under the influence generated by the parameters coming from the theory namely, $$\alpha $$ α , $$\beta $$ β , $$\gamma $$ γ , $$\delta $$ δ , everywhere within the astral fluid in the investigated high-density regime that supports the existence of realistic heavy pulsars such as PSR J0348+0432, PSR J0740+6620 and PSR J0030+0451.