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For a generalization to other types of scalar fields, see S. Hod and T. Piran, Phys. Rev. D 58, 044018 (1998) and references therein (for a massive scalar field)
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see also S. Hod, Phys. Rev. D 58, 104022 (1998), which, however, does not correctly handle the coupling between modes.
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Ref
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In Ref. 26 Hod recently analyzed the late time behavior of spin-(Formula presented) fields along the EH of a Kerr BH. However, his calculation was based on an assumption which (as we show at the end of this paper) turns out to be incorrect in the case (Formula presented) This led to an erroneous result in this case.
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Separate field equations for (Formula presented) and (Formula presented) were obtained in Ref
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Separate field equations for (Formula presented) and (Formula presented) were obtained in Ref. 5. A “unified” master equation for all spins s was first introduced by Bardeen and Press in Ref. 29.
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For further information about the late-time expansion see, e.g., Refs
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For further information about the late-time expansion see, e.g., Refs. 2411. (Note, however, the different notation in Ref. 24.)
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For a discussion of power series solutions near regular singular points of ordinary differential equations, see, for example, Sec. IV in H. Wayland, Differential Equations Applied in Science and Engineering (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1957)
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For a discussion of power series solutions near regular singular points of ordinary differential equations, see, for example, Sec. IV in H. Wayland, Differential Equations Applied in Science and Engineering (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1957).
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45
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or by referring to the limit (Formula presented) in the work by I. D. Novikov and A. A. Starobinsky, in Abstracts of Contributed Papers of the Ninth International Conference on General Relativity and Gravitation, Jena, 1980, p. 262
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Exact static solutions for a scalar field in Schwarzschild, expressed in terms of the Legendre functions, can be also obtained by referring to the limit (Formula presented) in Y. Gürsel, V. D. Sandberg, I. D. Novikov, and A. A. Starobinsky, Phys. Rev. D 19, 413 (1979);or by referring to the limit (Formula presented) in the work by I. D. Novikov and A. A. Starobinsky, in Abstracts of Contributed Papers of the Ninth International Conference on General Relativity and Gravitation, Jena, 1980, p. 262.
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and in W. H. Press and S. A. Teukolsky, Astrophys. J. 185, 649 (1973). A detailed review of this subject is provided in Secs. 70 and 81 of 31.
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