Areal Foliation and AVTD Behavior in T^2 Symmetric Spacetimes with Positive Cosmological Constant

We prove a global foliation result, using areal time, for T^2 symmetric spacetimes with a positive cosmological constant. We then find a class of solutions that exhibit AVTD behavior near the singularity.Comment: 15 pages, 0 figures, 2 references adde

Yang-Mills Flow and Uniformization Theorems

We consider a parabolic-like systems of differential equations involving geometrical quantities to examine uniformization theorems for two- and three-dimensional closed orientable manifolds. We find that in the two-dimensional case there is a simple gauge theoretic flow for a connection built from a Riemannian structure, and that the convergence of the flow to the fixed points is consistent with the Poincare Uniformization Theorem. We construct a similar system for the three-dimensional case. Here the connection is built from a Riemannian geometry, an SO(3) connection and two other 1-form fields which take their values in the SO(3) algebra. The flat connections include the eight homogeneous geometries relevant to the three-dimensional uniformization theorem conjectured by W. Thurston. The fixed points of the flow include, besides the flat connections (and their local deformations), non-flat solutions of the Yang-Mills equations. These latter "instanton" configurations may be relevant to the fact that generic 3-manifolds do not admit one of the homogeneous geometries, but may be decomposed into "simple 3-manifolds" which do.Comment: 21 pages, Latex, 5 Postscript figures, uses epsf.st

Degenerate neckpinches in Ricci flow

In earlier work, we derived formal matched asymptotic profiles for families of Ricci flow solutions developing Type-II degenerate neckpinches. In the present work, we prove that there do exist Ricci flow solutions that develop singularities modeled on each such profile. In particular, we show that for each positive integer $k\geq3$, there exist compact solutions in all dimensions $m\geq3$ that become singular at the rate (T-t)^{-2+2/k}$

Oscillatory approach to the singularity in vacuum T2T^2 symmetric spacetimes

A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.Comment: 2 pages submitted to the Ninth Marcel Grossmann Proceedings; v2, "all known cases" changed to "various known cases" in the first paragrap

Kidney disease in primary anti-phospholipid antibody syndrome

APS is an autoimmune disease defined by the presence of arterial or venous thrombotic events and/or pregnancy morbidity in patients who test positive for aPL. APS can be isolated (primary APS) or associated with other autoimmune diseases. The kidney is a major target organ in APS, and renal thrombosis can occur at any level within the vasculature of the kidney (renal arteries, intrarenal vasculature and renal veins). Histological findings vary widely, including ischaemic glomeruli and thrombotic lesions without glomerular or arterial immune deposits on immunofluorescence. Renal involvement in patients with definite APS is treated with long-term anticoagulants as warfarin, but new treatments are being tried. The aim of this article is to review the links between primary APS and kidney disease

The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory

A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.Comment: 7 pages includes 4 figures. Uses Revtex and psfig. Received "honorable mention" in 1998 Gravity Research Foundation essay contest. Submitted to Mod. Phys. Lett.

SLICC/ACR DAMAGE INDEX IS VALID, AND RENAL AND PULMONARY ORGAN SCORES ARE PREDICTORS OF SEVERE OUTCOME IN PATIENTS WITH SYSTEMIC LUPUS ERYTHEMATOSUS

We investigated the Systemic Lupus International Collaborative Clinics/American College of Rheumatology (SLICC/ACR) Damage Index as a predictor of severe outcome and an indicator of morbidity in different ethnic groups, and in regard to its validity. We retrospectively studied disease course within 10 yr of diagnosis in an inception cohort of 80 patients with systemic lupus erythematosus (SLE). The mean renal damage score (DS) at 1 yr after diagnosis was a significant predictor of endstage renal failure and the mean pulmonary DS at 1 yr significantly predicted death within 10 yr of diagnosis. Compared to Caucasians, Afro-Caribbeans and Asians had significantly higher mean total DS at 5 and 10 yr, and higher mean renal DS at 10 yr. At 5 yr, the mean renal DS in Afro-Caribbeans and the mean neuropsychiatric DS in Asians were significantly higher than in Caucasians. The rate of endstage renal failure in Caucasians was significantly lower than in the other ethnic groups. Our results confirm the validity of the SLICC/ACR Damage Inde

Numerical method for binary black hole/neutron star initial data: Code test

A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; Two of these are centered at the binary compact objects and cover a neighborhood of each object; the third patch extends to the asymptotic region. As in the Komatsu-Eriguchi-Hachisu method, nonlinear elliptic field equations are decomposed into a flat space Laplacian and a remaining nonlinear expression that serves in each iteration as an effective source. The equations are solved iteratively, integrating a Green's function against the effective source at each iteration. Detailed convergence tests for the essential part of the code are performed for a few types of selected Green's functions to treat different boundary conditions. Numerical computation of the gravitational potential of a fluid source, and a toy model for a binary black hole field are carefully calibrated with the analytic solutions to examine accuracy and convergence of the new code. As an example of the application of the code, an initial data set for binary black holes in the Isenberg-Wilson-Mathews formulation is presented, in which the apparent horizons are located using a method described in Appendix A.Comment: 19 pages, 18 figure

Fuchsian methods and spacetime singularities

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been recalled, various ways in which these equations have been applied in general relativity are described. Possible future applications are indicated