New class of regular and well behaved exact solutions in general relativity

Abstract

We present a new class of spherically symmetric regular and well behaved solutions of the general relativistic field equations in isotropic coordinates. These solutions describe perfect fluid balls with positively finite central pressure and positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The solutions of this class, the outmarch of pressure, density pressure-density ratio and the ratio of sound speed to light is monotonically decreasing. Keeping in view of well behaved nature in terms of central red shift and surface red shift and by assuming the surface density ρb=2×1014 g/cm3, we constructed a Neutral star model for k=2, resulting into maximum mass ≈6.36MΘ, linear dimension ≈48.08 km, surface red shift ≈1.132 and central red shift ≈17.1314.