Null hypersurfaces in generalized Robertson–Walker spacetimes

Null Screen Isoparametric Hypersurfaces in Lorentzian Space Forms

“…Based on these facts, the authors proved in [28,Prop. 5.2] the following relation between the shape operators (notice that a minus sign is missing in equation (19) there): For any X ∈ Γ(S * (T M )),…”

“…This article is organized as follows: in section 2 we introduce the preliminary results pertaining null submanifold theory, following closely the approach on [12,13]. Then on section 3 we use the transnormal approach developed in [28] to establish our framework for Generalized Robertson-Walker spacetimes. Finally, on section 4 we establish Cartan identities for null isoparametric hypersurfaces immersed in a Lorentzian space form and derive a local characterization result.…”

Null screen quasi-conformal hypersurfaces in semi-Riemannian manifolds and applications

“…Since A * ξ ξ = 0 and A N ξ = 0, we have the following relation between the shape operators (see the proof of Proposition 5.2 in [17]):…”

“…Example 5.4. In [17] the authors characterized the null totally umbilical hypersurfaces (M, g, S * (T M )) of Lorentzian space forms ( M n+2 c , ḡ) of non vanishing curvature and provided explicit examples with totally umbilical screen distribution S * (T M ) constructed from graphs. As an illustrative example, in de Sitter space -viewed as an hyperquadric in Lorentz-Minkowski space-consider the (signed) distance from any point p ∈ S n+1 to the "parallel" given by the set of points that make a constant angle θ = cos −1 α with respect to the fixed canonical vector e n+3 ∈ R n+3 1 .…”

Generalized Robertson-Walker Space-Time Admitting Evolving Null Horizons Related to a Black Hole Event Horizon

“…This class of space-time is inhomogeneous admitting an isotropic radiation whose subcase is classical Robertson-Walker (RW) space-time which includes Einstein-de-Sitter space-time, Friedman cosmological models, and the static Einstein space-time. Considerable work is available on GRW space-time, primarily on spacelike hypersurfaces [ 1 – 4 ] and more cited therein, and only recently there has been interest (see Kang [ 5 , 6 ] and Navarro et al [ 7 ]) on its null submanifold geometry. However, nothing much is available on physical application of their null hypersurfaces.…”