Geometry of crossing null shells

New geometric objects on null thin layers are introduced and their importance for crossing null-like shells are discussed. The Barrab\`es--Israel equations are represented in a new geometric form and they split into decoupled system of equations for two different geometric objects: tensor density ${\bf G}^a{_b}$ and vector field $I$. Continuity properties of these objects through a crossing sphere are proved. In the case of spherical symmetry Dray--t'Hooft--Redmount formula results from continuity property of the corresponding object.Comment: 24 pages, 1 figur

Energy-minimizing two black holes initial data

An attempt to construct the ``ground state'' vacuum initial data for the gravitational field surrounding two black holes is presented. The ground state is defined as the gravitational initial data minimizing the ADM mass within the class of data for which the masses of the holes and their distance are fixed. To parameterize different geometric arrangements of the two holes (and, therefore, their distance) we use an appropriately chosen scale factor. A method for analyzing the variations of the ADM mass and the masses (areas) of the horizons in terms of gravitational degrees of freedom is proposed. The Misner initial data are analyzed in this context: it is shown that they do not minimize the ADM mass.Comment: Minor corrections, 2 references adde

Dynamics of a self gravitating light-like matter shell: a gauge-invariant Lagrangian and Hamiltonian description

A complete Lagrangian and Hamiltonian description of the theory of self-gravitating light-like matter shells is given in terms of gauge-independent geometric quantities. For this purpose the notion of an extrinsic curvature for a null-like hypersurface is discussed and the corresponding Gauss-Codazzi equations are proved. These equations imply Bianchi identities for spacetimes with null-like, singular curvature. Energy-momentum tensor-density of a light-like matter shell is unambiguously defined in terms of an invariant matter Lagrangian density. Noether identity and Belinfante-Rosenfeld theorem for such a tensor-density are proved. Finally, the Hamiltonian dynamics of the interacting system: ``gravity + matter'' is derived from the total Lagrangian, the latter being an invariant scalar density.Comment: 20 pages, RevTeX4, no figure

Evidence that platelet-derived microvesicles may transfer platelet-specific immunoreactive antigens to the surface of endothelial cells and CD34+ hematopoietic stem/ progenitor cells--implication for the pathogenesis of immune thrombocytopenias.

The pathogenesis and tissue damage that accompanies destruction of platelets in immune thrombocytopenias (IT) is still not understood very well and in addition to platelets, other cells (e.g. endothelial cells, CD34+ hematopoietic stem/progenitors) may also become affected. Based on our previous work that platelet antigens (e.g., CD41) may be transferred by platelet-derived microvesicles (PMV) to the surface of other cells, we asked if platelet derived-antigens, especially those that are involved in the formation of anti-platelet antibodies in IT (e.g., against antigen HPA 1 a) could be also transferred by similar mechanism. To address this issue normal human CD34+ cells, human umbilical vein-endothelial cells (HUVEC) and monocytic cell line THP-1 were incubated with PMV derived from HPA1a+ donors. We noticed that the HPA1a antigen is highly expressed on PMV-derived from the HPAla positive platelets and is transferred in PMV-dependent manner to the surface of CD34+ cells, HUVEC and monocytic THP-1 cells. These cells covered with HPA1a positive PMV but not by PMV derived from HPAla negative platelets reacted with anti-HPA1a antibodies derived from the alloimmunized pregnant women. More importantly, human hematopoietic cells that were preincubated with HPA1a+ PMV and subsequently exposed to anti-HPA 1 a serum and human NK cells, become subject to elimination by antibody dependent cell cytotoxicity ADCC. Thus, we postulate that PMV-dependent transfer of antigens may playing an important role in "expanding" the population of target cells that may be affected by anti-platelet antibodies and explain several pathologies that accompany IT (e.g. damage of endothelium, cytopenias)

Rigid spheres in Riemannian spaces

Choice of an appropriate (3+1)-foliation of spacetime or a (2+1)-foliation of the Cauchy space, leads often to a substantial simplification of various mathematical problems in General Relativity Theory. We propose a new method to construct such foliations. For this purpose we define a special family of topological two-spheres, which we call "rigid spheres". We prove that there is a four-parameter family of rigid spheres in a generic Riemannian three-manifold (in case of the flat Euclidean three-space these four parameters are: 3 coordinates of the center and the radius of the sphere). The rigid spheres can be used as building blocks for various ("spherical", "bispherical" etc.) foliations of the Cauchy space. This way a supertranslation ambiguity may be avoided. Generalization to the full 4D case is discussed. Our results generalize both the Huang foliations (cf. \cite{LHH}) and the foliations used by us (cf. \cite{JKL}) in the analysis of the two-body problem.Comment: 23 page