We consider 5D Einstein-Maxwell-dilaton (EMd) gravity in spacetimes with three commuting Killing vectors: one timelike and two spacelike Killing vectors, one of which is hypersurface-orthogonal. Assuming a special ansatz for the Maxwell field we show that the 2-dimensional reduced EMd equations are completely integrable. We also develop a solution generating method for explicit construction of ...

I1 is shown thal for a given spherically symmelric disvibution of a perfect Huid on a spacelike hypersurface wiul boundary and a piven. time-dependent boundary prt?sure. there exis15 a unique, local-in-lime solution of the Einstein equations. A Schwmchild spacetime can be allached to h e Huid bady i f and only if the boundary prcssurc vanishes. We asume a smooth equation of slate for which UW d...

We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be constant near the gluing points, which was the case for previous such constructions. No global conditions on the initial data sets such as compactness, completeness...

We consider 5D Einstein-Maxwell (EM) gravity in spacetimes with three commuting Killing vectors: one timelike and two spacelike Killing vectors one of them being hypersurface-orthogonal. Assuming a special ansatz for the Maxwell field we show that the 2-dimensional reduced EM equations are completely integrable by deriving a Lax-pair presentation. We also develop a solution generating method fo...

A generalization of the limiting procedure of Penrose, which allows non-zero cosmological constants and takes into account metrics that contain homogeneous functions of degree zero, is presented. It is shown that any spacetime which admits a spacelike conformal Killing vector has a limit which is conformal to plane waves. If the spacetime is an Einstein space, its limit exists only if the cosmo...

Stationary, axisymmetric, vacuum, solutions of Einstein’s equations are obtained as critical points of the total mass among all axisymmetric and (t, φ) symmetric initial data with fixed angular momentum. In this variational principle, the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if an absolute minimum exists then it is equal to the ab...

In this paper, we study the intrinsic structures of high-dimensional data sets for analyzing their geometrical properties, where core message is hiding on some nonlinear manifolds. Using manifold learning technique with a particular focus mean curvature, develop new methods to investigate uniqueness constant curvature spacelike hypersurfaces in Lorentzian warped product Furthermore, extend stoc...

Abstract In this paper, we introduce the notion of a marginal tube, which is hypersurface foliated by surfaces. It generalises marginally trapped tube and several notions black hole horizons, for example trapping isolated dynamical etc. We prove that if every spacelike section surface, then null. There no assumption on topology tube. To it, study geometry surfaces in four-dimensional spacetime ...

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

In this paper, we try to give a classification of spacelike hypersurfaces the Lorentz-Minkowski space-time E1n+1, whose mean curvature vector field order (k+ 1) is an eigenvector kth linearized operator Lk, for non-negative integer k less than n. The Lk defined as linear part first variation (k + 1)th hypersurface arising from its normal variations. We show that any E1n+1 satisfying condition L...