Abstract
This paper deals with a family of lightlike (null) hypersurfaces (H u ) of a Lorentzian manifold M such that each null normal vector ℓ of H u is not entirely in H u , but, is defined in some open subset of M around H u . Although the family (H u ) is not unique, we show, subject to some reasonable condition(s), that the involved induced objects are independent of the choice of (H u ) once evaluated at u = constant. We use (n+1)-splitting Lorentzian manifold to obtain a normalization of ℓ and a well-defined projector onto H, needed for Gauss, Weingarten, Gauss-Codazzi equations and calculate induced metrics on proper totally umbilical and totally geodesic H u . Finally, we establish a link between the geometry and physics of lightlike hypersurfaces and a variety of black hole horizons.
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Duggal, K.L. Foliations of lightlike hypersurfaces and their physical interpretation. centr.eur.j.math. 10, 1789–1800 (2012). https://doi.org/10.2478/s11533-012-0067-x
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DOI: https://doi.org/10.2478/s11533-012-0067-x