Relativistic fluid spheres with particular application in cosmology and gravitational collapse

Abstract

A spherically symmetric comoving fluid solution of Einstein's equations is adapted for cosmological application by extending the geometry of standard FRW cosmology using a generalised curvature term. The resulting model retains many of the known cosmological properties including homogeneity of energy density, its relationship with internal pressure including equations of state, although in each case they have a generalised structure. It is shown that the adapted model does not require the inclusion of the arbitrary cosmological constant and the vacuum energy solution is discussed in its absence. The Hubble constant and deceleration parameter are also shown to have a form which characterises the modified geometry of the new model. These forms are calculated using current observational data and show how the standard cosmological geometry can be amended in a way which is consistent with an observed flat curvature and a decelerating universe. Finally the solution is also considered in the context of gravitational collapse where it is shown how fluids spheres obeying a central equation of state can be matched to empty spacetime.