DEGENERATE METRICS AND AN EMPTY BLACK-HOLE

Ashtekar's formulation of general relativity is polynomial, and admits degenerate 'metrics'. We consider 'metrics' which are everywhere degenerate on the initial data hypersurface. For a special class of them, we solve the constraint and evolution equations completely. Some 'neighbours' of the theory are briefly considered. We then consider spherically symmetric spacetimes. A general form of the stationary solutions, in terms of three arbitrary functions, without gauge fixing, is given for both degenerate and non-degenerate metrics. It is shown that the Schwarzschild solution may be joined smoothly to a degenerate solution across the event horizon, yielding a 'black hole' with a degenerate interior. Some comments on matter couplings are made.