Static Blackhole with Cosmological Influence: Whittaker Solutions

Abstract

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.