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Some Remarks on Gravitational Analogs of Magnetic Charge

C. G. Torre
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Abstract

Existing mathematical results are applied to the problem of classifying closed $p$-forms which are locally constructed from Lorentzian metrics on an $n$-dimensional orientable manifold $M$ ($0<p<n$). We show that the only closed, non-exact forms are generated by representatives of cohomology classes of $M$ and $(n-1)$-forms representing $n$-dimensional (with $n$ even) generalizations of the conservation of ``kink number'', which was exhibited by Finkelstein and Misner for $n=4$. The cohomology class that defines the kink number depends only on the diffeomorphism equivalence class of the metric, but a result of Gilkey implies that there is no representative of this cohomology class which is built from the metric, curvature and covariant derivatives of curvature to any finite order.

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C. G. Torre. 1994-11-07. Some Remarks on Gravitational Analogs of Magnetic Charge. https://doi.org/10.1088/0264-9381%2F12%2F6%2F001

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