null hypersurfaces
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Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 284
Author(s):  
Manuel Gutiérrez ◽  
Benjamín Olea

Starting from the main definitions, we review the rigging technique for null hypersurfaces theory and most of its main properties. We make some applications to illustrate it. On the one hand, we show how we can use it to show properties of null hypersurfaces, with emphasis in null cones, totally geodesic, totally umbilic, and compact null hypersurfaces. On the other hand, we show the interplay with the ambient space, including its influence in causality theory.


Author(s):  
Amrinder Pal Singh ◽  
Cyriaque Atindogbe ◽  
Rakesh Kumar ◽  
Varun Jain

We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared mean curvatures for a null hypersurface with a closed rigging of a Lorentzian space form and for a screen homothetic null hypersurface of a Lorentzian manifold. We also establish a generalized Chen–Ricci inequality for a screen homothetic null hypersurface of a Lorentzian manifold with a closed rigging for the hypersurface.


2021 ◽  
Vol 21 (2) ◽  
pp. 251-263
Author(s):  
C. Atindogbé ◽  
M. Gutiérrez ◽  
R. Hounnonkpe

Abstract We show how the topological and geometric properties of the family of null hypersurfaces in a Lorentzian manifold are related with the properties of the ambient manifold itself. In particular, we focus in how the presence of global symmetries and curvature conditions restrict the existence of compact null hypersurfaces. We use these results to show the influence on the existence of compact totally umbilic null hypersurfaceswhich are not totally geodesic. Finally we describe the restrictions that they impose in causality theory.


2020 ◽  
Vol 38 (4) ◽  
pp. 045018
Author(s):  
Michael T N Imseis ◽  
Abdulrahim Al Balushi ◽  
Robert B Mann

2020 ◽  
Vol 52 (10) ◽  
Author(s):  
David Hilditch ◽  
Juan A. Valiente Kroon ◽  
Peng Zhao

AbstractUsing the Newman–Penrose formalism we study the characteristic initial value problem in vacuum General Relativity. We work in a gauge suggested by Stewart, and following the strategy taken in the work of Luk, demonstrate local existence of solutions in a neighbourhood of the set on which data are given. These data are given on intersecting null hypersurfaces. Existence near their intersection is achieved by combining the observation that the field equations are symmetric hyperbolic in this gauge with the results of Rendall. To obtain existence all the way along the null-hypersurfaces themselves, a bootstrap argument involving the Newman–Penrose variables is performed.


2020 ◽  
Vol 155 ◽  
pp. 103751
Author(s):  
Shintaro Akamine ◽  
Atsufumi Honda ◽  
Masaaki Umehara ◽  
Kotaro Yamada

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