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On Uniqueness of the Kerr‐Newman Black Holes
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9.and R. Price (to be published).
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18.See, e.g., R. Courant and D. Hilbert, Method of Mathematical Physics (Interscience, New York, 1962), Vol. II, p. 321.
19.To verify explicitly that analyticity of the Kruskal components implies analyticity of set [where u,v are the standard Kruskal coordinates of the Schwarzschild metric ], and set Analyticity of directly implies analyticity of and where is analytic in and in a region containing the exterior region and horizon of [In terms of the Schwarzschild radial coordinate, r, ]. This implies analyticity of and hence of and With this established it is easy to verify that and must also be analytic.
20.The series for must converge because the series for converges (by hypothesis) and must have finite mass. Similarly, the series for and must converge. For the case of one can show that the effect of the sequence of coordinate transformations on must converge, but this does not imply in an immediately obvious fashion that the series itself must converge and, in fact, the remote possibility that it does not converge has not as yet been rigorously ruled out.
21.J. Bekenstein (to be published).
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