Isolated black holes have been the subject of extensive studies. Spacetimes associated with these black holes are asymptotically flat and time-independent. On the other hand, a realistic situation may require that the black holes be imbedded in a cosmological background or be surrounded by a local mass distribution. Under these circumstances, one has to consider black holes in non-flat backgrounds, relaxing one or both of the above mentioned conditions, namely asymptotic flatness and time-independence. Very little research has been done in this area either at the conceptual level or by studying specific examples.

As an initial step towards the exploration of black holes in non-flat backgrounds, we explored models which dispense with asymptotic flatness while retaining time-independence. These were obtained as special cases of the McVittie model of 1933 for a body in an expanding universe, which turned out to be unsuitable, and Vaidya's ``Kerr metric in a cosmological background''. From the latter, the non-spinning non-expanding case was shown to represent a black hole in a perfect fluid background.

In this example it proved possible to match the solution to a spherically symmetric vacuum (Schwarzschild) black hole, giving a limit on the black hole mass and resolving, for this example, questions about the nature of the horizon, thermodynamics and so on. The resulting metric has a singularity antipodal to the black hole but this can removed by matching to an Einstein universe. The behaviour of scalar wave perturbations to this solution was studied; in particular the stability and scattering properties were investigated. A paper on these results is in preparation.

We started to look at the spinning case. The energy-momentum external to the black hole has terms for which we are seeking a physical model, and we are also working on matching to a vacuum black hole (Kerr) interior. This work will be continued in future collaboration.

A long list of issues for further investigation was clarified.

(A fuller version of this report, and the preprint of the associated paper, are available on request to M.A.H.MacCallum@qmul.ac.uk)