Some Curvature Problems in Semi-Riemannian Geometry

In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the construction of Lorentzian metrics which satisfy the dominant energy condition.Comment: 25 pages, LaTeX, 4 figure

On the existence of topological hairy black holes in SU(N) EYM theory with a negative cosmological constant

We investigate the existence of black hole solutions of four dimensional su(N) EYM theory with a negative cosmological constant. Our analysis differs from previous works in that we generalise the field equations to certain non-spherically symmetric spacetimes. We prove the existence of non-trivial solutions for any integer N, with N−1 gauge degrees of freedom. Specifically, we prove two results: existence of solutions for fixed values of the initial parameters and as |Λ|→∞, and existence of solutions for any Λ<0 in some neighbourhood of existing trivial solutions. In both cases we can prove the existence of `nodeless' solutions, i.e. such that all gauge field functions have no zeroes; this fact is of interest as we anticipate that some of them may be stable

Albumin reduces blood-brain barrier permeability but does not alter infarct size in a rat model of neonatal stroke

Human serum albumin therapy confers neurobehavioral and histopathologic neuroprotection in adult stroke models. We investigated whether albumin might also be neuroprotective in ischemic brain injury using a transient filament middle cerebral artery occlusion (tfMCAO) model in 10-d-old rat pups treated with 0.25% albumin or saline 1 h after reperfusion. We performed serial neurobehavioral and magnetic resonance imaging (MRI) assessments immediately after tfMCAO (day 0) and on 1, 3, 7, 14, and 28 d. IgG staining to assess blood-brain barrier (BBB) integrity and standard histology was obtained on 1, 3, and 28 d. Hemispheric infarct volumes from MRI were similar in saline and albumin groups (0 h: 39% and 44%; d 1: 46% and 55%; and d 28:10% and 24%) as were neurobehavioral assessments. IgG staining at 3 d post-ischemia showed loss of BBB integrity that was significantly reduced after albumin. Elevated T2 values suggesting vasogenic edema was seen in albumin compared with saline-treated animals, as was increased water mobility (i.e. increased apparent diffusion coefficient (ADC) reflecting cytotoxic edema. The reasons why albumin was not neuroprotective in neonatal stroke compared with adults remain uncertain. Effective strategies in adult models need to be reassessed in the neonate