On the existence of Kundt's metrics and degenerate (or extremal) Killing horizons

Details On the existence of Kundt's metrics and degenerate (or extremal) Killing horizons On the existence of Kundt's metrics and degenerate (or extremal) Killing horizons

Feb 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cqgra..26c5011j&link_type=abstract

Classical and Quantum Gravity, Volume 26, Issue 3, pp. 035011 (2009).

Computer Science

1

Scientific paper

It is shown that Kundt's metric for vacuum cannot be constructed when two-dimensional spacelike sections of null hypersurfaces are compact, connected manifolds with no boundary unless they are tori or spheres, i.e. higher genus g >= 2 is excluded by vacuum Einstein equations. The so-called basic equation (resulting from Einstein equations) is examined. This is a nonlinear PDE for an unknown covector field and an 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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