Black Holes in Non-flat Backgrounds: the Schwarzschild Black Hole in the Einstein Universe

TL;DR

This paper constructs a composite static spacetime combining Schwarzschild and Vaidya metrics to model a black hole in the Einstein universe background, analyzing scalar wave behavior in this non-flat setting.

Contribution

It introduces a novel composite model of a black hole in a non-flat background by matching Schwarzschild and Vaidya spacetimes with an Einstein universe, ensuring a non-singular exterior.

Findings

The exterior scale length limits black hole mass.

Scalar waves exhibit specific behaviors in the composite spacetime.

The model provides insights into black holes in non-flat cosmological backgrounds.

Abstract

As an example of a black hole in a non-flat background a composite static spacetime is constructed. It comprises a vacuum Schwarzschild spacetime for the interior of the black hole across whose horizon it is matched on to the spacetime of Vaidya representing a black hole in the background of the Einstein universe. The scale length of the exterior sets a maximum to the black hole mass. To obtain a non-singular exterior, the Vaidya metric is matched to an Einstein universe. The behaviour of scalar waves is studied in this composite model.