  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.
