  In this article, we investigate the impact of cosmological parameters on
black holes using an exact solution to Einstein's equations that satisfies the
Whittaker equation of state. We examine a spherically symmetric black hole in
the background of a static Einstein Universe with a perfect fluid source with
the cosmological constant. This solution is characterized by two independent
parameters, namely the size of the universe~($R$) and the cosmological
constant~(Lambda), representing the cosmological influences. We explore
phenomena such as periastron precession and the scattering of massless scalar
fields to determine how these cosmological parameters affect the physics around
black holes.
