Axisymmetric stationary solutions with arbitrary multipole moments

In this paper, the problem of finding an axisymmetric stationary spacetime from a specified set of multipole moments, is studied. The condition on the multipole moments, for existence of a solution, is formulated as a convergence condition on a power series formed from the multipole moments. The methods in this paper can also be used to give approximate solutions to any order as well as estimates on each term of the resulting power series.Comment: 12 page

Calculation of, and bounds for, the multipole moments of stationary spacetimes

In this paper the multipole moments of stationary asymptotically flat spacetimes are considered. We show how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on R^2. We also give a bound on the multipole moments. This gives a proof of the "necessary part" of a long standing conjecture due to Geroch.Comment: 11 page

Static axisymmetric space-times with prescribed multipole moments

In this article we develop a method of finding the static axisymmetric space-time corresponding to any given set of multipole moments. In addition to an implicit algebraic form for the general solution, we also give a power series expression for all finite sets of multipole moments. As conjectured by Geroch we prove in the special case of axisymmetry, that there is a static space-time for any given set of multipole moments subject to a (specified) convergence criterion. We also use this method to confirm a conjecture of Hernandez-Pastora and Martin concerning the monopole-quadropole solution.Comment: 14 page

Report on workshop A1: Exact solutions and their interpretation

I report on the communications and posters presented on exact solutions and their interpretation at the GRG18 Conference, Sydney.Comment: 9 pages, no figures. Many typos corrected. Report submitted to the Proceedings of GR18. To appear in CQ

On the construction of a geometric invariant measuring the deviation from Kerr data

This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set corresponds to data for the Kerr spacetime, and thus, it characterises this type of data. The construction presented is valid for boosted and non-boosted initial data sets which are, in a sense, asymptotically Schwarzschildean. As a preliminary step to the construction of the geometric invariant, an analysis of a characterisation of the Kerr spacetime in terms of Killing spinors is carried out. A space spinor split of the (spacetime) Killing spinor equation is performed, to obtain a set of three conditions ensuring the existence of a Killing spinor of the development of the initial data set. In order to construct the geometric invariant, we introduce the notion of approximate Killing spinors. These spinors are symmetric valence 2 spinors intrinsic to the initial hypersurface and satisfy a certain second order elliptic equation ---the approximate Killing spinor equation. This equation arises as the Euler-Lagrange equation of a non-negative integral functional. This functional constitutes part of our geometric invariant ---however, the whole functional does not come from a variational principle. The asymptotic behaviour of solutions to the approximate Killing spinor equation is studied and an existence theorem is presented.Comment: 36 pages. Updated references. Technical details correcte

Deficiency and Also Transgenic Overexpression of Timp-3 Both Lead to Compromised Bone Mass and Architecture In Vivo

Tissue inhibitor of metalloproteinases-3 (TIMP-3) regulates extracellular matrix via its inhibition of matrix metalloproteinases and membrane-bound sheddases. Timp-3 is expressed at multiple sites of extensive tissue remodelling. This extends to bone where its role, however, remains largely unresolved. In this study, we have used Micro-CT to assess bone mass and architecture, histological and histochemical evaluation to characterise the skeletal phenotype of Timp-3 KO mice and have complemented this by also examining similar indices in mice harbouring a Timp-3 transgene driven via a Col-2a-driven promoter to specifically target overexpression to chondrocytes. Our data show that Timp-3 deficiency compromises tibial bone mass and structure in both cortical and trabecular compartments, with corresponding increases in osteoclasts. Transgenic overexpression also generates defects in tibial structure predominantly in the cortical bone along the entire shaft without significant increases in osteoclasts. These alterations in cortical mass significantly compromise predicted tibial load-bearing resistance to torsion in both genotypes. Neither Timp-3 KO nor transgenic mouse growth plates are significantly affected. The impact of Timp-3 deficiency and of transgenic overexpression extends to produce modification in craniofacial bones of both endochondral and intramembranous origins. These data indicate that the levels of Timp-3 are crucial in the attainment of functionally-appropriate bone mass and architecture and that this arises from chondrogenic and osteogenic lineages

Generation of a genomic tiling array of the human Major Histocompatibility Complex (MHC) and its application for DNA methylation analysis

Background: The major histocompatibility complex (MHC) is essential for human immunity and is highly associated with common diseases, including cancer. While the genetics of the MHC has been studied intensively for many decades, very little is known about the epigenetics of this most polymorphic and disease-associated region of the genome.Methods: To facilitate comprehensive epigenetic analyses of this region, we have generated a genomic tiling array of 2 Kb resolution covering the entire 4 Mb MHC region. The array has been designed to be compatible with chromatin immunoprecipitation (ChIP), methylated DNA immunoprecipitation (MeDIP), array comparative genomic hybridization (aCGH) and expression profiling, including of non-coding RNAs. The array comprises 7832 features, consisting of two replicates of both forward and reverse strands of MHC amplicons and appropriate controls.Results: Using MeDIP, we demonstrate the application of the MHC array for DNA methylation profiling and the identification of tissue-specific differentially methylated regions (tDMRs). Based on the analysis of two tissues and two cell types, we identified 90 tDMRs within the MHC and describe their characterisation.Conclusion: A tiling array covering the MHC region was developed and validated. Its successful application for DNA methylation profiling indicates that this array represents a useful tool for molecular analyses of the MHC in the context of medical genomics