The picture of black holes we have drawn so far changes drastically if quantum effects are taken into account. Before we go into the details of this in Section 5 of this chapter, we want to make a few general remarks on the interplay of Relativity Theory and Quantum Theory. For a more detailed discussion we refer the reader to the literature given at the end of the chapter.

The problem

The General Theory of Relativity is completely compatible with all other classical theories. Even if the details of the coupling of a classical field (Maxwell, Dirac, neutrino or Klein–Gordon field) to the metric field are not always free of arbitrariness and cannot yet be experimentally tested with sufficient accuracy, no doubt exists as to the inner consistency of the procedure.

This optimistic picture becomes somewhat clouded when one appreciates that besides the gravitational field the only observable classical field in our universe is the Maxwell field, while the many other interactions between the building blocks of matter can only be described with the aid of Quantum Theory. A unification of Relativity Theory and Quantum theory has not yet been achieved, however.

One of the main postulates of relativity theory is that a locally geodesic coordinate system can be introduced at every point of space-time, so that the action of the gravitational force becomes locally ineffective and the space is approximately a Minkowski space. Hence it is easily understandable why in our neighbourhood, with its relatively small space curvature, space is, to very good approximation, as it is assumed to be in quantum theory.