1. This statement is also known as the «Israel-Carter conjecture». See, for example,C. W. Misner, K. S. Thorne andJ. A. Wheeler:Gravitation (University of Maryland Press, College Park, Md., 1970). Preliminary Edition.
2. J. A. Wheeler:Transcending the law of conservation of leptons, Report at theCortona International Conference on Astrophysical Consequences of the Weak Interactions (June 12, 1970).
3. J. B. Hartle: Contribution inMagic without Magic: John Archibald Wheeler, ed. byJ. C. Klauder, W. H. Freeman and Company (1972), and alsoPhys. Rev., D3, 2938 (1971). I am greatly indebted to Prof.Hartle for letting me know about his work prior to publication and also for illuminating discussions. His methods were of great value in obtaining the results reported in this note.
4. Equation (2) was given byJ. B. Hartle:Phys. Rev., D1, 394 (1970).
5. For the theory of the Dirac equation in curved space, seeV. Bargmann:Sitzber. Preuss. Akad. Wiss., Phys. Math. Kl., 346 (1932). For a lucid review and applications to neutrinos, seeD. R. Brill andJ. A. Wheeler:Rev. Mod. Phys.,29, 465 (1957).