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    Comparison of general relativistic polytropic and adiabatic fluid spheres with a repulsive cosmological constant

    Zdeněk Stuchlík · Prosinec 01, 2004 · Fyzika · 0 comments
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    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;

    https://ui.adsabs.harvard.edu/abs/2004ragt.meet…75H

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