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Generalization of the ``Schwarzschild Surface'' to Arbitrary Static and Stationary Metrics
1.D. Finkelstein, Phys. Rev. 110, 965 (1958).
2.B. Carter (report of work prior to publication).
3.J. Ehlers in Gravitation: An Introduction to Current Research, Louis Witten, Ed. (John Wiley & Sons, Inc., New York, 1962).
4.Square brackets denote antisymmetrization: We use a metric with signature − + + +.
5.This is shown by a well‐known computation , using the (Killing) antisymmetry of and the geodesic equation for
6.G. Salzman and A. H. Taub, Phys. Rev. 95, 1959 (1954).
7.See Theorem 5.1 in S. Sternberg, Lectures on Differential Geometry (Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1964)
7.or Theorem 8‐4 in L. Auslander and R. E. MacKenzie, Introduction to Differentiate Manifolds (McGraw‐Hill Book Company, Inc., New York, 1963). Sufficient for our purposes here is also a comment on p. 105
7.in J. A. Schouten, Ricci Calculus (Springer‐Verlag, Berlin, 1954), 2nd ed.
8.Some of the basic equations in this section have been taken from the preprint “Maximal Analytic Extension of the Kerr Metric” by R. H. Boyer and R. W. Lindquist. See also R. H. Boyer and T. G. Price, Proc. Camb. Phil. Soc. 61, 531 (1965).
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