The aim of this paper is to show how we can induce contact structures, contact metric structures and Sasaki structures on a null hypersurface from a rigging vector field. We give several explicit examples of this construction and some obstructions to its existence. For example, contact metric structures can be introduced only on zero null mean curvature null hypersurfaces, whereas Sasaki structures can only be introduced in totally geodesic ones. In particular we show how we can construct a Kahler halo around an isolated horizon of a black hole. We also study the stability of the construction. We prove that close enough contact metric (resp. Sasaki) structures can be connected by a one parameter family of contact metric (resp. Sasaki) structures.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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Elsevier
