Perfect fluid spheres with cosmological constant

TL;DR

This paper explores static perfect fluid spheres with a cosmological constant, deriving new solutions, analyzing their properties, and using numerical methods to study realistic equations of state.

Contribution

It introduces new exact solutions involving the Nariai metric and generalizes the Einstein static universe with non-constant density and pressure.

Findings

Conditions for vanishing pressure surface derived

Numerical integration confirms solutions with realistic equations of state

Pressure surface can be located in regions with decreasing area orbits

Abstract

We examine static perfect fluid spheres in the presence of a cosmological constant. New exact matter solutions are discussed which require the Nariai metric in the vacuum region. We generalize the Einstein static universe such that neither its energy density nor its pressure is constant throughout the spacetime. Using analytical techniques we derive conditions depending on the equation of state to locate the vanishing pressure surface. This surface can in general be located in regions with decreasing area group orbits. We use numerical methods to integrate the field equations for realistic equations of state and find consistent results.