Static Blackhole with Cosmological Influence: Whittaker Solutions

TL;DR

This paper explores how cosmological parameters like the universe's size and the cosmological constant influence black hole physics, using an exact Einstein's equations solution with applications to phenomena such as precession and scalar field scattering.

Contribution

It introduces a new exact solution to Einstein's equations incorporating cosmological influences on black holes, analyzing their effects on specific physical phenomena.

Findings

Cosmological parameters affect black hole precession.

Scalar field scattering is influenced by the universe's size and Lambda.

The solution provides insights into black hole behavior in a cosmological context.

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.