Lectures on Linear Stability of Rotating Black Holes

These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and work out the connection to conservation laws. The Penrose process and superradiance effects are discussed. Decay results on the long-time behavior of Dirac waves are outlined. It is explained schematically how the Maxwell equations and the equations for linearized gravitational waves can be decoupled to obtain the Teukolsky equation. It is shown how the Teukolsky equation can be fully separated to a system of coupled ordinary differential equations. Linear stability of the non-extreme Kerr black hole is stated as a pointwise decay result for solutions of the Cauchy problem for the Teukolsky equation. The stability proof is outlined, with an emphasis on the underlying ideas and methods.Comment: 25 pages, LaTeX, 3 figures, lectures given at first DOMOSCHOOL in July 2018, minor improvements (published version

Black Holes in Modified Gravity (MOG)

The field equations for Scalar-Tensor-Vector-Gravity (STVG) or modified gravity (MOG) have a static, spherically symmetric black hole solution determined by the mass $M$ with two horizons. The strength of the gravitational constant is $G=G_N(1+\alpha)$ where $\alpha$ is a parameter. A regular singularity-free MOG solution is derived using a nonlinear field dynamics for the repulsive gravitational field component and a reasonable physical energy-momentum tensor. The Kruskal-Szekeres completion of the MOG black hole solution is obtained. The Kerr-MOG black hole solution is determined by the mass $M$, the parameter $\alpha$ and the spin angular momentum $J=Ma$. The equations of motion and the stability condition of a test particle orbiting the MOG black hole are derived, and the radius of the black hole photosphere and the shadows cast by the Schwarzschild-MOG and Kerr-MOG black holes are calculated. A traversable wormhole solution is constructed with a throat stabilized by the repulsive component of the gravitational field.Comment: 14 pages, 3 figures. Upgraded version of paper to match published version in European Physics Journal

Porosities of building limestones: using the solid density to assess data quality

A good knowledge of the volume-fraction porosity is essential in any technical work on porous materials. In construction materials the porosity is commonly measured by the Archimedes buoyancy method, from which the bulk density of the test specimen is also obtained. The porosity and the bulk density together fix the solid density of the specimen, as only two of the three quantities are independent. The solid density, although rarely discussed, is determined by the mineralogy of the specimen, and therefore can provide a valuable check on the accuracy of porosity and bulk density measurements. Our analysis of published data on calcitic limestones shows that the solid density is generally close to the ideal crystallographic density of calcite. Small deviations can often be traced to variations in mineral composition. However some published porosity–density data are inconsistent with the known mineralogy. Deviations which cannot be ascribed to composition may be assumed to arise from measurement errors. We show the value of using the solid density as a quality check on the measured porosity. We recommend that the solid density should always be calculated for this purpose when the Archimedes method is used. This check can be useful also when porosities are measured by helium pycnometry or by mercury intrusion porosimetry

PD-1 Regulates Neural Damage in Oligodendroglia-Induced Inflammation

We investigated the impact of immune regulatory mechanisms involved in the modulation of the recently presented, CD8+ lymphocyte mediated immune response in a mouse model of oligodendropathy-induced inflammation (PLPtg-mutants). The focus was on the role of the co-inhibitory molecule PD-1, a CD28-related receptor expressed on activated T- and B-lymphocytes associated with immune homeostasis and autoimmunity. PLPtg/PD-1-deficient double mutants and the corresponding bone marrow chimeras were generated and analysed using immunohistochemistry, light- and electron microscopy, with particular emphasis on immune-cell number and neural damage. In addition, the immune cells in both the CNS and the peripheral immune system were investigated by IFN-gamma elispot assays and spectratype analysis. We found that mice with combined pathology exhibited significantly increased numbers of CD4+ and CD8+ T-lymphocytes in the CNS. Lack of PD-1 substantially aggravated the pathological phenotype of the PLPtg mutants compared to genuine PLPtg mutants, whereas the PD-1 deletion alone did not cause alterations in the CNS. CNS T-lymphocytes in PLPtg/PD-1-/- double mutants exhibited massive clonal expansions. Furthermore, PD-1 deficiency was associated with a significantly higher propensity of CNS but not peripheral CD8+ T-cells to secrete proinflammatory cytokines. PD-1 could be identified as a crucial player of tissue homeostasis and immune-mediated damage in a model of oligodendropathy-induced inflammation. Alterations of this regulatory pathway lead to overt neuroinflammation of high pathogenetic impact. Our finding may have implications for understanding the mechanisms leading to the high clinical variability of polygenic or even monogenic disorders of the nervous system

Mouse models for preeclampsia: disruption of redox-regulated signaling

The concept that oxidative stress contributes to the development of human preeclampsia has never been tested in genetically-defined animal models. Homozygous deletion of catechol-Omethyl transferase (Comt-/-) in pregnant mice leads to human preeclampsia-like symptoms (high blood pressure, albuminurea and preterm birth) resulting from extensive vasculo-endothelial pathology, primarily at the utero-fetal interface where maternal cardiac output is dramatically increased during pregnancy. Comt converts estradiol to 2-methoxyestradiol 2 (2ME2) which counters angiogenesis by depleting hypoxia inducible factor-1 alpha (HIF-1 alpha) at late pregnancy. We propose that in wild type (Comt++) pregnant mice, 2ME2 destabilizes HIF-1 alpha by inhibiting mitochondrial superoxide dismutase (MnSOD). Thus, 2ME2 acts as a pro-oxidant, disrupting redox-regulated signaling which blocks angiogenesis in wild type (WT) animals in physiological pregnancy. Further, we suggest that a lack of this inhibition under normoxic conditions in mutant animals (Comt-/-) stabilises HIF-1 alpha by inactivating prolyl hydroxlases (PHD). We predict that a lack of inhibition of MnSOD, leading to persistent accumulation of HIF-1 alpha, would trigger inflammatory infiltration and endothelial damage in mutant animals. Critical tests of this hypothesis would be to recreate preeclampsia symptoms by inducing oxidative stress in WT animals or to ameliorate by treating mutant mice with Mn-SOD-catalase mimetics or activators of PHD

Diagnostic and preventive service trends in private general practice: 1983-1984 to 1998-1999

The document attached has been archived with permission from the Australian Dental Association. An external link to the publisher’s copy is included.Background: Aggregate trends have indicated increases in the provision of diagnostic and preventive services but there have been few reports based on their component sub-categories. The aims of this study were to investigate time trends in the provision of sub-categories of diagnostic and preventive services across a 15-year period. Methods: A random sample of Australian dentists was surveyed by mailed questionnaire in 1983-1984, 1988-1989, 1993-1994 and 1998-1999 (response rates 71-75 per cent). Data were weighted to provide representative estimates for the age by sex distribution of private general practitioners in 1983, 1988, 1993 and 1998. Results: Rates per visit were higher, Poisson regression, P<0.05, in 1998-1999 compared to baseline for examinations, radiographs, prophylaxis and topical fluoride. Diagnostic and preventive service rates varied by age of patient: compared to patients aged 65+ years, examinations were higher among children aged <5 years to adults aged 25-44 years, radiographs were lower among children <5 years and 5-11 years but higher among adults aged from 18-24 years to 45-64 years, prophylaxis services were lower among children <5 years but higher among adolescents 12-17 years to adults aged 45-64 years, while topical fluoride was higher among children 5-11 years and adolescents 12-17 years. Conclusions: Examination, radiograph, prophylaxis, and topical fluoride rates increased over the study period. While examination rates increased for both children and adults, and prophylaxis rates increased for adolescents and adults, rates for radiographs and topical fluoride only increased for adults. Agespecific changes in service rates over time indicate the effect of changing oral health status and population demographics on service provision.DS Brennan, AJ Spence

Deformation of Codimension-2 Surface and Horizon Thermodynamics

The deformation equation of a spacelike submanifold with an arbitrary codimension is given by a general construction without using local frames. In the case of codimension-1, this equation reduces to the evolution equation of the extrinsic curvature of a spacelike hypersurface. In the more interesting case of codimension-2, after selecting a local null frame, this deformation equation reduces to the well known (cross) focusing equations. We show how the thermodynamics of trapping horizons is related to these deformation equations in two different formalisms: with and without introducing quasilocal energy. In the formalism with the quasilocal energy, the Hawking mass in four dimension is generalized to higher dimension, and it is found that the deformation of this energy inside a marginal surface can be also decomposed into the contributions from matter fields and gravitational radiation as in the four dimension. In the formalism without the quasilocal energy, we generalize the definition of slowly evolving future outer trapping horizons proposed by Booth to past trapping horizons. The dynamics of the trapping horizons in FLRW universe is given as an example. Especially, the slowly evolving past trapping horizon in the FLRW universe has close relation to the scenario of slow-roll inflation. Up to the second order of the slowly evolving parameter in this generalization, the temperature (surface gravity) associated with the slowly evolving trapping horizon in the FLRW universe is essentially the same as the one defined by using the quasilocal energy.Comment: Latex, 61 pages, no figures; v2, type errors corrected; v3, references and comments are added, English is improved, to appear in JHE

Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region

The thrust distribution in electron-positron annihilation is a classical precision QCD observable. Using renormalization group (RG) evolution in Laplace space, we perform the resummation of logarithmically enhanced corrections in the dijet limit, $T\to 1$ to next-to-next-to-leading logarithmic (NNLL) accuracy. We independently derive the two-loop soft function for the thrust distribution and extract an analytical expression for the NNLL resummation coefficient $g_3$. To combine the resummed expressions with the fixed-order results, we derive the $\log(R)$-matching and $R$-matching of the NNLL approximation to the fixed-order NNLO distribution.Comment: 50 pages, 12 figures, 1 table. Few minor changes. Version accepted for publication in JHE

Stationary Black Holes: Uniqueness and Beyond

The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.Comment: Major update of the original version by Markus Heusler from 1998. Piotr T. Chru\'sciel and Jo\~ao Lopes Costa succeeded to this review's authorship. Significantly restructured and updated all sections; changes are too numerous to be usefully described here. The number of references increased from 186 to 32