Relativistic fluid spheres with particular application in cosmology and gravitational collapse

TL;DR

This paper develops a modified cosmological model based on a spherically symmetric fluid solution of Einstein's equations, which aligns with observations without requiring a cosmological constant, and explores gravitational collapse scenarios.

Contribution

It introduces a generalized curvature extension to standard FRW cosmology, eliminating the need for a cosmological constant and analyzing gravitational collapse within this framework.

Findings

Model matches current observational data for flat universe and deceleration.

Provides a generalized structure for energy density and pressure relations.

Shows how fluid spheres can be matched to empty spacetime in collapse scenarios.

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.