**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;