Isotropic Durgapal IV fluid sphere in bigravity

Abstract

We analyze an isotropic uncharged fluid sphere model within bigravity considering the Durgapal IV metric (M.C. Durgapal, J. Phys. A: Math. Gen. 15, 2637 (1982)). In this work, we investigate the effects of the scale parameter k on the local matter distribution. Here, we have chosen the compact star candidate SMC X-1 with observed values of mass = (1.29 ± 0.05) M⊙ and radius [Formula: see text] km, respectively, to analyze our results analytically as well as graphically. For smaller values of k, we get the stiff (or hard) equation of state (EoS). Here, we solve the modified Einstein field equations in the presence of the background metric γμν. Due to this constant curvature background, the density and pressure terms are modified by adding an extra term, which affects the EoS. For r ≪ k, the background de Sitter space–time reduces into Minkowski form, and the coupling vanishes. We discuss certain physical quantities of our obtained solution, such as density, isotropic pressure, sound speed, pressure-density gradients, compactness, and surface redshift, to claim the physical viability of our model. It is found that our model clearly satisfies all the energy conditions, the causality condition, and the dynamical equilibrium via a modified Tolman–Oppenheimer–Volkov equation. Finally, we can conclude that our proposed model is physically realistic and well behaved.