15 research outputs found
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 with conformally
invariant differential . We provide two criteria: If is real
analytic, 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, 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, openâlabel, twoâarm study
evaluating the safety and efficacy of eculizumab in preventing acute antibodyâ
mediated rejection (AMR) in sensitized recipients of livingâdonor kidney transplants
requiring pretransplant desensitization (NCT01399593). In total, 102 patients underâ
went desensitization. Posttransplant, 51 patients received standard of care (SOC)
and 51 received eculizumab. The primary end point was week 9 posttransplant treatâ
ment failure rate, a composite of: biopsyâproven acute AMR (Banff 2007 grade II or
III; assessed by blinded central pathology); graft loss; death; or loss to followâup. 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 outâ
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 livingâdonor kidney
transplants (EudraCT 2010â019630â28)
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/