We study imbedded general hypersurfaces in spacetime i.e. hypersurfaces whose timelike, spacelike or null character can change from point to point.Inherited geometrical structures on these hypersurfaces are defined by two distinct methods: the first one, in which a rigging vector (a vector not tangent to the hypersurface anywhere) induces the standard rigged connection; and the other one, more ...

The geometry of the Sagnac effect in a stationary region spacetime is reviewed with aim emphasizing role asymmetry Finsler metric defined on spacelike hypersurface associated to splitting and related future-pointing null geodesics spacetime. We show also that an analogous comes into play for timelike geodesics.

We study the mean curvature flow in 3-dimensional null hypersurfaces. In a spacetime hypersurface is called null, if its induced metric degenerate. The speed of spacelike surfaces projection codimension-two vector onto hypersurface. impose fairly mild conditions on Then for an outer un-trapped initial surface, condition which resembles mean-convexity surface Euclidean space, we prove that exist...

We show that static electro–vacuum black hole space–times containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non–degenerate components of the event horizon do not exist. This is done by a careful study of the near-horizon geometry of degenerate horizons, which allows us to eliminate the last restriction of the static electro-vacuum no-hai...

The relativistic kinetic equations for two domains separated by a hypersurface with both spacelike and timelike parts are derived. The particle exchange between the domains separated by timelike boundaries generates source terms and modifies the collision term of the kinetic equation. The correct hydrodynamic equations for the "hydro+cascade" models are obtained and their differences from exist...

The initial-value problem is posed by giving a conformal three-metric on each of two nearby spacelike hypersurfaces, their proper-time separation up to a multiplier to be determined, and the mean (extrinsic) curvature of one slice. The resulting equations have the same elliptic form as does the one-hypersurface formulation. The metrical roots of this form are revealed by a conformal " thin sand...

We show that static electrovacuum black hole spacetimes containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non-degenerate components of the event horizon do not exist, under the supplementary hypothesis that all degenerate components of the event horizon have charges of the same sign. This extends previous uniqueness theorems of Simon and...

In this paper we study the uniqueness of complete noncompact spacelike hypersurfaces immersed in generalized Robertson-Walker (GRW) spacetimes. According to a suitable restriction on the higher order mean curvature and the norm of the gradient of the height function of the hypersurface, we obtain some rigidity theorems in GRW spacetimes. Besides, we establish nonparametric results on the entire...

We consider the general orthogonal metric separable in space and time variables in comoving coordinates. We then characterise perfect fluid models admitted by such a metric. It turns out that the homogeneous models can only be either FLRW or Bianchi I while the inhomogeneous ones can only admit G2 (two mutually as well as hypersurface orthogonal spacelike Killing vectors) isometry. The latter c...

The initial-value problem is posed by giving a conformal three-metric on each of two nearby spacelike hypersurfaces, their proper-time separation up to a multiplier to be determined, and the mean (extrinsic) curvature of one slice. The resulting equations have the same elliptic form as does the one-hypersurface formulation. The metrical roots of this form are revealed by a conformal " thin sand...