**Publication date:** Dec 2004

**Abstract:**

Solutions of general relativistic field equations for static, spherically symmetric, equilibrium perfect-fluid configurations obeying the polytropic and adiabatic equation of state in the presence of a repulsive cosmological constant are discussed. The influence of the cosmological constant on the total mass of the configurations, their radius and the profiles of energy density, rest energy density, pressure and metric coefficients is studied and compared for the polytropic and adiabatic case. The static equilibrium configurations are allowed for σ<σ_{crit} (α<α_{crit}), where the critical values σ_{crit} (α_{crit}) of the relativity parameter σ (α) ≡ pcent/rhocent c^{2} of the polytropes (adiabates) depend on the cosmological constant and the polytropic index n of the equation of state and can be determined by a numerical procedure. The numerical results show that for sufficiently small values of the relativity parameter σ=α≪ σ_{crit}, the polytropic spheres are more compact than the adiabatic ones. Increase of the cosmological constant causes increase of both the radius and mass of the spheres and makes the profiles of the metric coefficients flatter. For large values of the relativity paramater, σ=α≲ σ_{crit}, the situation is more complex and depends also on the value of the polytropic parameter n. The mass of the adiabatic spheres can exceed the mass of the polytropes for n≳ 2. In the case of n=3, the adiabatic spheres can even be more compact than the polytropic ones. Generally, the role of the cosmological constant is supressed with both σ=α and n growing.
**Authors:**

Hledík, Stanislav; Stuchlík, Zdeněk; Mrázová, Kristina;