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As an example of a black hole in a non-flat background a composite staticspacetime is constructed. It comprises a vacuum Schwarzschild spacetime for theinterior of the black hole across whose horizon it is matched on to thespacetime of Vaidya representing a black hole in the background of the Einsteinuniverse. The scale length of the exterior sets a maximum to the black holemass. To obtain a non-singular exterior, the Vaidya metric is matched to anEinstein universe. The behaviour of scalar waves is studied in this compositemodel.Comment: 8 pages, 3 postscript figures, minor corrections Journal Ref:  accepted for Physical Review

Black holes in nonflat backgrounds: The Schwarzschild black hole in the Einstein universe