In this paper, we compute the Frenet vectors and the curvatures of the spacelike intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space E 1 .

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or light-like, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermediate parts where the mean curvature vector fie...

The outward–pointing principal null direction of the Schwarzschild Rie-mann tensor is null hypersurface–forming. If the Schwarzschild mass spontaneously jumps across one such hypersurface then the hypersurface is the history 1 of an outgoing light–like shell. The outward– pointing principal null direction of the Kerr Riemann tensor is asymptotically (in the neighbourhood of future null infinity...

The discovery by Gott of a remarkably simple spacetime with closed timelike curves (CTC’s) provides a tool for investigating how the creation of time machines is prevented in classical general relativity. The Gott spacetime contains two infinitely long, parallel cosmic strings, which can equivalently be viewed as point masses in (2+1)-dimensional gravity. We examine the possibility of building ...

The recently constructed two dimensional Sen connection is applied in the problem of quasilocal energy-momentum in general relativity. First it is shown that, because of one of the two 2 dimensional Sen–Witten identities, Penrose’s quasi-local charge integral can be expressed as a Nester–Witten integral. Then, to find the appropriate spinor propagation laws to the Nester– Witten integral, all t...

In the present paper a global conformal invariant Y of a closed initial data set is constructed. A spacelike hypersurface in a Lorentzian spacetime naturally inherits from the spacetime metric a diierentiation D e , the so-called real Sen connection, which turns out to be determined completely by the initial data h ab and ab induced on , and coincides, in the case of vanishing second fundamenta...

The Newman-Penrose constants of the spacetime corresponding to the development of the Brill-Lindquist initial data are calculated by making use of a particular representation of spatial infinity due to H. Friedrich. The Brill-Lindquist initial data set represents the head-on collision of two non-rotating black holes. In this case one non-zero constant is obtained. Its value is given in terms of...

The quantization of Lorentzian or Euclidean 2+1 gravity by canonical methods is a well-studied problem. However, the constraints of 2+1 gravity are those of a topological field theory and therefore resemble very little those of the corresponding Lorentzian 3+1 constraints. In this paper we canonically quantize Euclidean 2+1 gravity for arbitrary genus of the spacelike hypersurface with new, cla...