**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;