MG11 
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Dynamical stability of fluid spheres in spacetimes with a nonzero cosmological constant

We determine the equation governing small radial oscillations and related Sturm-Liouville eigenvalue problem for eigenmodes of the oscillations in the case of spherically symmetric configurations of perfect fluid in spacetimes with a nonzero cosmological constant. Uniform-density and polytropic cases are investigated. It is shown that repulsive cosmological constant rises the critical adiabatic index and decreases the critical radius under which the dynamical instability occurs.