CONSTRAINT ALGEBRA OF DEGENERATE RELATIVITY

As shown by Ashtekar in the mid 80s, general relativity can be extende d to incorporate degenerate metrics. This extension is not unique, how ever, as one can change the form of the Hamiltonian constraints and ob tain an alternative degenerate extension of general relativity that di sagrees with Ashtekar's original theory when the triads vectors are de generate. In this paper, the constraint algebra of a particular altern ative theory is explicitly evaluated and compared with that of Ashteka r's original degenerate extension. A generic classification of the dif ference between the two theories is given in terms of the degeneracy a nd surface-forming properties of the triad vectors. (This classificati on is valid when the degeneracy and surface-forming properties of the triad vectors is the same everywhere in an open set about a point in s pace.) If the triad vectors are degenerate and surface-forming, then a ll the secondary constraints of the alternative degenerate extension a re satisfied as a consequence of the primary constraints, and the cons traints of this theory are weaker than those of Ashtekar's. If the deg enerate triad vectors are not surface-forming, then the first secondar y constraint of the alternative theory already implies equivalence wit h Ashtekar's degenerate extension. What happens when the degeneracy an d surface-forming properties of the triad vectors change from point to point is an open question.