Foliation of the Kottler-Schwarzschild-De Sitter Spacetime by Flat Spacelike Hypersurfaces

There exist Kruskal like coordinates for the Reissner-Nordstrom (RN) black hole spacetime which are regular at coordinate singularities. Non existence of such coordinates for the extreme RN black hole spacetime has already been shown. Also the Carter coordinates available for the extreme case are not manifestly regular at the coordinate singularity, therefore, a numerical procedure was developed to obtain free fall geodesics and flat foliation for the extreme RN black hole spacetime. The Kottler-Schwarzschild-de Sitter (KSSdS) spacetime geometry is similar to the RN geometry in the sense that, like the RN case, there exist non-singular coordinates when there are two distinct coordinate singularities. There are no manifestly regular coordinates for the extreme KSSdS case. In this paper foliation of all the cases of the KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a non-singular time coordinate.Comment: 12 pages, 4 figure

The developmental pathway for CD103(+)CD8+ tissue-resident memory T cells of skin

Tissue-resident memory T cells (T(RM) cells) provide superior protection against infection in extralymphoid tissues. Here we found that CD103(+)CD8(+) T(RM) cells developed in the skin from epithelium-infiltrating precursor cells that lacked expression of the effector-cell marker KLRG1. A combination of entry into the epithelium plus local signaling by interleukin 15 (IL-15) and transforming growth factor-β (TGF-β) was required for the formation of these long-lived memory cells. Notably, differentiation into T(RM) cells resulted in the progressive acquisition of a unique transcriptional profile that differed from that of circulating memory cells and other types of T cells that permanently reside in skin epithelium. We provide a comprehensive molecular framework for the local differentiation of a distinct peripheral population of memory cells that forms a first-line immunological defense system in barrier tissues.Supported by National Health and Medical Research Council of Australia and Australian Research Council