Investigation of all Ricci semi-symmetric and all conformally semi-symmetric spacetimes

We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. We verify that only conformally flat spacetimes can be Ricci semi-symmetric without being conformally semi-symmetric and show that only vacuum spacetimes and spacetimes with just a $\Lambda$-term can be Ricci semi-symmetric without being conformally semi-symmetric.Comment: 4 pages, 1 tabl

Geometry of Higher-Dimensional Black Hole Thermodynamics

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstr\"om (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for $d=5$ Kerr black hole is curved and divergent in the extremal limit. For $d \geq 6$ Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In $d \geq 5$ the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in $d=5$ with double angular momenta.Comment: 8 pages, 2 figures, RevTex, References adde

Where are the trapped surfaces?

We discuss the boundary of the spacetime region through each point of which a trapped surface passes, first in some simple soluble examples, and then in the self-similar Vaidya solution. For the latter the boundary must lie strictly inside the event horizon. We present a class of closed trapped surfaces extending strictly outside the apparent horizon.Comment: 6 pages, 1 figure; talk at the Spanish Relativity Meeting ERE09 in Bilba

Anti-de Sitter Quotients, Bubbles of Nothing, and Black Holes

In 3+1 dimensions there are anti-de quotients which are black holes with toroidal event horizons. By analytic continuation of the Schwarzschild-anti-de Sitter solution (and appropriate identifications) one finds two one parameter families of spacetimes that contain these quotient black holes. One of these families consists of B-metrics ("bubbles of nothing"), the other of black hole spacetimes. All of them have vanishing conserved charges.Comment: 14 pages, 3 figures. References added, one explanation improve

Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein-Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Comment: 14 pages, one figure. Dedicated to Rafael Sorkin's birthda

The PTPN22 C1858T gene variant is associated with proinsulin in new-onset type 1 diabetes

<p>Abstract</p> <p>Background</p> <p>The protein tyrosine phosphatase nonreceptor type 2 (<it>PTPN22</it>) has been established as a type 1 diabetes susceptibility gene. A recent study found the C1858T variant of this gene to be associated with lower residual fasting C-peptide levels and poorer glycemic control in patients with type 1 diabetes. We investigated the association of the C1858T variant with residual beta-cell function (as assessed by stimulated C-peptide, proinsulin and insulin dose-adjusted HbA_1c), glycemic control, daily insulin requirements, diabetic ketoacidosis (DKA) and diabetes-related autoantibodies (IA-2A, GADA, ICA, ZnT8Ab) in children during the first year after diagnosis of type 1 diabetes.</p> <p>Methods</p> <p>The C1858T variant was genotyped in an international cohort of children (n = 257 patients) with newly diagnosed type 1 diabetes during 12 months after onset. We investigated the association of this variant with liquid-meal stimulated beta-cell function (proinsulin and C-peptide) and antibody status 1, 6 and 12 months after onset. In addition HbA_1cand daily insulin requirements were determined 1, 3, 6, 9 and 12 months after diagnosis. DKA was defined at disease onset.</p> <p>Results</p> <p>A repeated measurement model of all time points showed the stimulated proinsulin level is significantly higher (22%, p = 0.03) for the T allele carriers the first year after onset. We also found a significant positive association between proinsulin and IA levels (est.: 1.12, p = 0.002), which did not influence the association between <it>PTPN22 </it>and proinsulin (est.: 1.28, p = 0.03).</p> <p>Conclusions</p> <p>The T allele of the C1858T variant is positively associated with proinsulin levels during the first 12 months in newly diagnosed type 1 diabetes children.</p

On explicit thermodynamic functions and extremal limits of Myers–Perry black holes

We study thermodynamic geometries of Myers–Perry (MP) black holes with arbitrary number of angular momenta. This geometric method allows us to visualize thermodynamic state spaces of the MP black holes as wedges embedded in a Minkowski-like parameter space. The opening angles of these wedges are uniquely determined by the number of spacetime dimensions d, and the number of angular momenta associated with the MP black holes, n. The geometric structure captures extremal limits of the MP black holes, and hence serves as a method for identifying the black hole’s extremal limit. We propose that classification of the MP black hole solutions should based on these uncovered structures. In order for the ultraspinning regime to exist, at least one of the angular momenta has to be set to zero. Finally, we conjecture that the membrane phase of ultraspinning MP black holes is reached at the minimum temperature in the case where 2n<d−3 based on the thermodynamic curvature obtained