A rigidity property of asymptotically simple spacetimes arising from conformally flat data

Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data coincides with Schwarzschild data near infinity.Comment: 37 page

Conformal structures of static vacuum data

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity. The tendency of these singularities to spread along the null generators of null infinity obstructs the development of a smooth conformal structure at null infinity. For the solution-jets arising from time reflection symmetric data to extend smoothly to the critical sets it is necessary that the Cotton tensor of the initial three-metric h satisfies a certain conformally invariant condition (*) at space-like infinity, it is sufficient that h be asymptotically static at space-like infinity. The purpose of this article is to characterize the gap between these conditions. We show that with the class of metrics which satisfy condition (*) on the Cotton tensor and a certain non-degeneracy requirement is associated a one-form $\kappa$ with conformally invariant differential $d\kappa$. We provide two criteria: If $h$ is real analytic, $\kappa$ is closed, and one of it integrals satisfies a certain equation then h is conformal to static data near space-like infinity. If h is smooth, $\kappa$ is asymptotically closed, and one of it integrals satisfies a certain equation asymptotically then h is asymptotically conformal to static data at space-like infinity.Comment: 68 pages, typos corrected, references and details adde

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

Safety and efficacy of eculizumab in the prevention of antibody-mediated rejection in living-donor kidney transplant recipients requiring desensitization therapy: A randomized trial

We report results of a phase 2, randomized, multicenter, open‐label, two‐arm study evaluating the safety and efficacy of eculizumab in preventing acute antibody‐ mediated rejection (AMR) in sensitized recipients of living‐donor kidney transplants requiring pretransplant desensitization (NCT01399593). In total, 102 patients under‐ went desensitization. Posttransplant, 51 patients received standard of care (SOC) and 51 received eculizumab. The primary end point was week 9 posttransplant treat‐ ment failure rate, a composite of: biopsy‐proven acute AMR (Banff 2007 grade II or III; assessed by blinded central pathology); graft loss; death; or loss to follow‐up. Eculizumab was well tolerated with no new safety concerns. No significant difference in treatment failure rate was observed between eculizumab (9.8%) and SOC (13.7%; P = .760). To determine whether data assessment assumptions affected study out‐ come, biopsies were reanalyzed by central pathologists using clinical information. The resulting treatment failure rates were 11.8% and 21.6% for the eculizumab and SOC groups, respectively (nominal P = .288). When reassessment included grade I AMR, the treatment failure rates were 11.8% (eculizumab) and 29.4% (SOC; nominal P = .048). This finding suggests a potential benefit for eculizumab compared with SOC in preventing acute AMR in recipients sensitized to their living‐donor kidney transplants (EudraCT 2010‐019630‐28)

Numerical relativity simulations in the era of the Einstein Telescope

Numerical-relativity (NR) simulations of compact binaries are expected to be an invaluable tool in gravitational-wave (GW) astronomy. The sensitivity of future detectors such as the Einstein Telescope (ET) will place much higher demands on NR simulations than first- and second-generation ground-based detectors. We discuss the issues facing compact-object simulations over the next decade, with an emphasis on estimating where the accuracy and parameter space coverage will be sufficient for ET and where significant work is needed. <br/