Maximal Hypersurfaces and Positivity of Mass

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Proof of the Thin Sandwich Conjecture

We prove that the Thin Sandwich Conjecture in general relativity is valid, provided that the data $(g_{ab},\dot g_{ab})$ satisfy certain geometric conditions. These conditions define an open set in the class of possible data, but are not generically satisfied. The implications for the ``superspace'' picture of the Einstein evolution equations are discussed.Comment: 8 page

Tetrads in SU(3) X SU(2) X U(1) Yang-Mills geometrodynamics

The relationship between gauge and gravity amounts to understanding underlying new geometrical local structures. These structures are new tetrads specially devised for Yang-Mills theories, Abelian and Non-Abelian in four-dimensional Lorentzian spacetimes. In the present manuscript a new tetrad is introduced for the Yang-Mills SU(3) X SU(2) X U(1) formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations. New theorems are proved regarding isomorphisms between local internal SU(3) X SU(2) X U(1) groups and local tensor products of spacetime LB1 and LB2 groups of transformations. The new tetrads and the stress-energy tensor allow for the introduction of three new local gauge invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for the gauge invariant diagonalization of the Yang-Mills stress-energy tensor is developed.Comment: There is a new appendix. The unitary transformations by local SU(2) subgroup elements of a local group coset representative is proved to be a new local group coset representative. This proof is relevant to the study of the memory of the local tetrad SU(3) generated gauge transformations. Therefore, it is also relevant to the group theorems proved in the paper. arXiv admin note: substantial text overlap with arXiv:gr-qc/060204

Cosmological spacetimes not covered by a constant mean curvature slicing

We show that there exist maximal globally hyperbolic solutions of the Einstein-dust equations which admit a constant mean curvature Cauchy surface, but are not covered by a constant mean curvature foliation.Comment: 11 page

Heat flow method to Lichnerowicz type equation on closed manifolds

In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -\Delta u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\geq0$ are given smooth functions. Our analysis is based on the global existence of positive solutions to the following heat equation {ll} u_t-\Delta u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M\times\mathbb{R}^{+}, u(x,0)=u_0,\quad in\quad M with the positive smooth initial data $u_0$.Comment: 10 page

Functional interaction between the ZO-1-interacting transcription factor ZONAB/DbpA and the RNA processing factor symplekin

Epithelial tight junctions participate in the regulation of gene expression by controlling the activity of transcription factors that can interact with junctional components. One such protein is the Y-box transcription factor ZONAB/DbpA that binds to ZO-1, a component of the junctional plaque. Symplekin, another nuclear protein that can associate with tight junctions, functions in the regulation of polyadenylation and thereby promotes gene expression. Here, we addressed the question of whether these two proteins interact and whether this is of functional relevance. We demonstrate that ZONAB/DbpA and symplekin form a complex in kidney and intestinal epithelial cells that can be immunoprecipitated and that exists in the nucleus. The interaction between ZONAB/DbpA and symplekin can be reconstituted with recombinant proteins. In reporter gene assays in which ZONAB/DbpA functions as a repressor, symplekin functionally interacts with ZONAB/DbpA, indicating that symplekin can also promote transcriptional repression. RNAi experiments indicate that symplekin depletion reduces the nuclear accumulation and the transcriptional activity of ZONAB/DbpA in colon adenocarcinoma cells, resulting in inhibition of proliferation and reduced expression of the ZONAB/DbpA-target gene cyclin D1. Our data thus indicate that symplekin and ZONAB/DbpA cooperate in the regulation of transcription, and that they promote epithelial proliferation and cyclin D1 expression

Sur la positivité de la masse

Nous démontrons qu'il existe un voisinage (au sens d'espaces fonctionnels convenables) de l'espace-temps de Minkovoski tel que tout espace-temps de ce voisinage, solution des équations d'Einstein du vide, a une masse positive. Nous indiquons quelques résultats et difficultés pour la résolution du probléme global

Existence and uniqueness of Bowen-York Trumpets

We prove the existence of initial data sets which possess an asymptotically flat and an asymptotically cylindrical end. Such geometries are known as trumpets in the community of numerical relativists.Comment: This corresponds to the published version in Class. Quantum Grav. 28 (2011) 24500

`Mass without mass' from thin shells in Gauss-Bonnet gravity

Five tensor equations are obtained for a thin shell in Gauss-Bonnet gravity. There is the well known junction condition for the singular part of the stress tensor intrinsic to the shell, which we also prove to be well defined. There are also equations relating the geometry of the shell (jump and average of the extrinsic curvature as well as the intrinsic curvature) to the non-singular components of the bulk stress tensor on the sides of the thin shell. The equations are applied to spherically symmetric thin shells in vacuum. The shells are part of the vacuum, they carry no energy tensor. We classify these solutions of `thin shells of nothingness' in the pure Gauss-Bonnet theory. There are three types of solutions, with one, zero or two asymptotic regions respectively. The third kind of solution are wormholes. Although vacuum solutions, they have the appearance of mass in the asymptotic regions. It is striking that in this theory, exotic matter is not needed in order for wormholes to exist- they can exist even with no matter.Comment: 13 pages, RevTex, 8 figures. Version 2: includes discussion on the well-defined thin shell limit. Version 3: typos fixed, a reference added, accepted for publication in Phys. Rev.

On the local existence of maximal slicings in spherically symmetric spacetimes

In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.Comment: 4 pages. Accepted for publication in Journal of Physics: Conference Series, Proceedings of the Spanish Relativity Meeting ERE200