Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors

We consider source-free electromagnetic fields in spacetimes possessing a non-null Killing vector field, $\xi^a$. We assume further that the electromagnetic field tensor, $F_{ab}$, is invariant under the action of the isometry group induced by $\xi^a$. It is proved that whenever the two potentials associated with the electromagnetic field are functionally independent the entire content of Maxwell's equations is equivalent to the relation \n^aT_{ab}=0. Since this relation is implied by Einstein's equation we argue that it is enough to solve merely Einstein's equation for these electrovac spacetimes because the relevant equations of motion will be satisfied automatically. It is also shown that for the exceptional case of functionally related potentials \n^aT_{ab}=0 implies along with one of the relevant equations of motion that the complementary equation concerning the electromagnetic field is satisfied.Comment: 7 pages,PACS numbers: 04.20.Cv, 04.20.Me, 04.40.+

The Evolving Role of Opioid Treatment in Chronic Pain Management

Opioids for chronic pain management have become increasingly controversial, yet many patients continue to be treated with high doses for prolonged periods of time. The miscon‐ ception between patients and providers alike is that these drugs can be taken without conse‐ quences. This liberalized thinking is far from the clinical practice of just two decades ago

Global Extensions of Spacetimes Describing Asymptotic Final States of Black Holes

We consider a globally hyperbolic, stationary spacetime containing a black hole but no white hole. We assume, further, that the event horizon, \tn, of the black hole is a Killing horizon with compact cross-sections. We prove that if surface gravity is non-zero constant throughout the horizon one can {\it globally} extend such a spacetime so that the image of $\cal N$ is a proper subset of a regular bifurcate Killing horizon in the enlarged spacetime. The necessary and sufficient conditions are given for the extendibility of matter fields to the enlarged spacetime. These conditions are automatically satisfied if the spacetime is static (and, hence ``$t$"-reflection symmetric) or stationary-axisymmetric with ``$t-\phi$" reflection isometry and the matter fields respect the reflection isometry. In addition, we prove that a necessary and sufficient condition for the constancy of the surface gravity on a Killing horizon is that the exterior derivative of the twist of the horizon Killing field vanish on the horizon. As a corollary of this, we recover a result of Carter that constancy of surface gravity holds for any black hole which is static or stationary- axisymmetric with the ``$t-\phi$" reflection isometry. No use of Einstein's equation is made in obtaining any of the above results. Taken together, these results support the view that any spacetime representing the asymptotic final state of a black hole formed by gravitational collapse may be assumed to possess a bifurcate Killing horizon or a Killing horizon with vanishing surface gravity.Comment: 20 pages, plain te

CD4 T cells remain the major source of HIV-1 during end stage disease.

OBJECTIVE: To assess the source of HIV-1 production in lymphoid tissue biopsies from HIV-infected patients, with no prior anti-retroviral protease inhibitor treatment, with a CD4 cell count > 150 x 10(6)/l (group I) or < 50 x 10(6)/l (group II), co-infected with Mycobacterium tuberculosis or Mycobacterium avium complex. DESIGN AND METHODS: Lymphoid tissue biopsies from 11 HIV-1-infected patients, taken for diagnostic purposes, were studied by HIV-1 RNA in situ hybridization and immunohistochemistry. RESULTS: Patients of group I showed well organized granulomas, in contrast with patients of group II, in which granuloma formation was absent. HIV-1 RNA-positive cells in group I patients were found mainly around the granulomas, whereas in group II HIV-1-producing cells were confined to areas with remaining intact lymphoid tissue. Despite the abundant presence of macrophages, the productively infected HIV-1-positive cells in both groups were almost exclusively CD4 T cells. CONCLUSION: In contrast with previously published data, CD4 T cells appear to remain the major source of HIV-1 production in end-stage disease

Organization of the Arp2/3 Complex in Hippocampal Spines

Changes in the morphology of a dendritic spine require remodeling of its actin-based cytoskeleton. Biochemical mechanisms underlying actin remodeling have been studied extensively, but little is known about the physical organization of the actin-binding proteins that mediate remodeling in spines. Long-term potentiation-inducing stimuli trigger expansion of the spine head, suggesting local extension and branching of actin filaments. Because filament branching requires the Arp2/3 complex, we used quantitative immunoelectron microscopy to elucidate the organization of ARPC-2 (Arp2/3 complex subunit 2), an essential component of the complex. Our data from CA1 hippocampus indicate that Arp2/3 concentrates within spines in a previously unrecognized torroidal domain, apparently specialized to mediate actin filament branching

Quasi-local rotating black holes in higher dimension: geometry

With a help of a generalized Raychaudhuri equation non-expanding null surfaces are studied in arbitrarily dimensional case. The definition and basic properties of non-expanding and isolated horizons known in the literature in the 4 and 3 dimensional cases are generalized. A local description of horizon's geometry is provided. The Zeroth Law of black hole thermodynamics is derived. The constraints have a similar structure to that of the 4 dimensional spacetime case. The geometry of a vacuum isolated horizon is determined by the induced metric and the rotation 1-form potential, local generalizations of the area and the angular momentum typically used in the stationary black hole solutions case.Comment: 32 pages, RevTex

A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric

A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is ``rotating''--i.e., is such that the stationary Killing field is not everywhere normal to the horizon--must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, $P$. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. However, in spacetimes of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator. In this paper, we prove that, nevertheless, a higher dimensional stationary black hole that is rotating must be axisymmetric. No assumptions are made concerning the topology of the horizon cross-sections other than that they are compact. However, we assume that the horizon is non-degenerate and, as in the 4-dimensional proof, that the spacetime is analytic.Comment: 24 pages, no figures, v2: footnotes and references added, v3: numerous minor revision

Exact Results for a Three-Body Reaction-Diffusion System

A system of particles hopping on a line, singly or as merged pairs, and annihilating in groups of three on encounters, is solved exactly for certain symmetrical initial conditions. The functional form of the density is nearly identical to that found in two-body annihilation, and both systems show non-mean-field, ~1/t**(1/2) instead of ~1/t, decrease of particle density for large times.Comment: 10 page