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Manifolds in the Schwarzschild and Kerr metrics - MaRDI portal

Manifolds in the Schwarzschild and Kerr metrics (Q752519)

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scientific article; zbMATH DE number 4178071
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English
Manifolds in the Schwarzschild and Kerr metrics
scientific article; zbMATH DE number 4178071

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    Manifolds in the Schwarzschild and Kerr metrics (English)
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    1990
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    The reviewer can not understand this paper. The author's abstract says ``We show that the Schwarzschild and Kerr metrics can be derived on any Riemannian manifold. Since any differentiable manifolds can be given a Riemann metric, we conclude that the Schwarzschild and Kerr metrics hold on differentiable manifolds in general.'' Only the first phrase of the second sentence has a definite meaning and is, in fact, false. A (connected, Hausdorff) manifold must be paracompact (or, equivalently, second countable) before it admits a positive definite metric and, in addition, must admit a 1-dimensional distribution in order to admit a Lorentz metric. The (two pages) of the paper are littered with typographical errors, spelling mistakes, undefined symbols and the like, together with several bewildering statements. The reviewer can make no further sensible comment.
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