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

Pre-diagnostic serum concentrations of organochlorines and risk of acute myeloid leukemia: A nested case-control study in the Norwegian Janus Serum Bank Cohort

Background: Epidemiologic studies suggest an increased risk of leukemia among individuals occupationally exposed to some organochlorine (OC) compounds. Associations between serum OC pesticide and polychlorinated biphenyl (PCB) levels and risk of acute myeloid leukemia (AML), the most common subtype of acute leukemia in adult populations, have not been evaluated prospectively in the general population. Objective: We evaluated the risk of AML in relation to pre-diagnostic serum levels of OC pesticides and PCBs in a case-control study nested within the Janus Serum Bank Cohort. Methods: Janus is a large population-based cohort containing biologic samples collected beginning in the early 1970s from ~318,000 individuals in Norway. Serum levels of 11 OC pesticides or their metabolites and 34 PCB congeners were measured in 56 AML cases and 288 controls. Conditional logistic regression was conducted to evaluate associations between lipid-adjusted serum OC levels and risk of AML. Results: Higher serum levels of total chlordane/heptachlor metabolites were associated with AML risk (3rd vs. 1st tertile odds ratio (OR) = 2.26, 95% confidence interval (CI) = 0.91–5.63; ptrend = 0.11). Significant exposure-response associations were observed for levels of heptachlor epoxide (3rd vs. 1st tertile OR = 2.85, 95% CI = 1.05–7.73; ptrend = 0.02) and dieldrin (3rd vs. 1st tertile OR = 2.71, 95% CI = 1.07–6.83; ptrend = 0.03). No significant exposure-response associations with AML risk were observed for total DDT or individual isomers and derivatives. Higher serum levels of p,p′-DDT showed a non-significant increase in risk, but the exposure-response became attenuated when co-adjusting for heptachlor epoxide or dieldrin levels. Serum PCB levels were not significantly associated with AML risk. Conclusions: Our data suggest that higher serum levels of dieldrin and metabolites derived from chlordane/heptachlor are associated with risk of AML in the general Norwegian population, based on samples collected on average ~17 years before diagnosis. Further research in populations with historically high or recent exposure to DDT is warranted to assess the association with AML risk with body burden of specific DDT isomers and derivatives