On a family of well behaved perfect fluid balls as astrophysical objects in general relativity

Abstract

A family of well behaved perfect fluid balls has been derived starting with the metric potential g44=B(1+Cr2)n for all positive integral values of n. For n≥4, the members of this family are seen to satisfy the various physical conditions e.g. c2ρ≥p≥0,dp/dr 1. Also the pressure, energy density, velocity of sound and ratio of pressure and energy density are of monotonically decreasing towards the pressure free interface (r=a). The fluid balls join smoothly with the Schwarzschild exterior model at r=a. The well behaved perfect fluid balls so obtained are utilised to construct the superdense star models with their surface density 2×1014 gm/cm3. We have found that the maximum mass of the fluid balls corresponding to various values of n are decreasing with the increasing values of n. Over all maximum mass for the whole family turns out to be 4.1848MΘ and the corresponding radius as 19.4144 km while the red shift at the centre and red shift at surface as Z0=1.6459 and Za=0.6538 respectively this all happens for n=4. It is interesting to note that for higher values of n viz n≥170, the physical data start merging with that of Kuchowicz superdense star models and hence the family of fluid models tends to the Kuchowicz fluid models as n→∞. Consequently the maximum mass of the family of solution can not be less than 1.6096 MΘ which is the maximum mass occupied by the Kuchowicz superdense ball. Hence each member of the family for n≥4 provides the astrophysical objects like White dwarfs, Quark star, typical neutron star.