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arXiv · 0806.0518

On the existence of Kundt's metrics with compact sections of null hypersurfaces

Jacek Jezierski
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Abstract

It is shown that Kundt's metric for vacuum cannot be constructed when two-dimensional space-like sections of null hypersurfaces are compact, connected manifolds with no boundary unless they are tori or spheres, i.e. higher genus $\mathbf{g} \geq 2$ is excluded by vacuum Einstein equations. The so-called {\em basic equation} (resulting from Einstein equations) is examined. This is a non-linear PDE for unknown covector field and unknown Riemannian structure on the two-dimensional manifold. It implies several important results derived in this paper. It arises not only for Kundt's class but also for degenerate Killing horizons and vacuum degenerate isolated horizons.

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Jacek Jezierski. 2008-06-03. On the existence of Kundt's metrics with compact sections of null hypersurfaces. https://doi.org/10.1063/1.3141307

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