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

Kerr-AdS and its Near-horizon Geometry: Perturbations and the Kerr/CFT Correspondence

We investigate linear perturbations of spin-s fields in the Kerr-AdS black hole and in its near-horizon geometry (NHEK-AdS), using the Teukolsky master equation and the Hertz potential. In the NHEK-AdS geometry we solve the associated angular equation numerically and the radial equation exactly. Having these explicit solutions at hand, we search for linear mode instabilities. We do not find any (non-)axisymmetric instabilities with outgoing boundary conditions. This is in agreement with a recent conjecture relating the linearized stability properties of the full geometry with those of its near-horizon geometry. Moreover, we find that the asymptotic behaviour of the metric perturbations in NHEK-AdS violates the fall-off conditions imposed in the formulation of the Kerr/CFT correspondence (the only exception being the axisymmetric sector of perturbations).Comment: 26 pages. 4 figures. v2: references added. matches published versio

Mycobacterium avium-intracellulare cellulitis occurring with septic arthritis after joint injection: a case report

BACKGROUND: Cellulitis caused by Mycobacterium avium-intracellulare has rarely been described. Mycobacterium avium-intracellulare is a rare cause of septic arthritis after intra-articular injection, though the causative role of injection is difficult to ascertain in such cases. CASE PRESENTATION: A 57-year-old with rheumatoid arthritis treated with prednisone and azathioprine developed bilateral painful degenerative shoulder arthritis. After corticosteroid injections into both acromioclavicular joints, he developed bilateral cellulitis centered over the injection sites. Skin biopsy showed non-caseating granulomas, and culture grew Mycobacterium avium-intracellulare. Joint aspiration also revealed Mycobacterium avium-intracellulare infection. CONCLUSION: Although rare, skin and joint infections caused by Mycobacterium avium-intracellulare should be considered in any immunocompromised host, particularly after intra-articular injection. Stains for acid-fast bacilli may be negative in pathologic samples even in the presence of infection; cultures of tissue specimens should always be obtained

Drinking behaviour and alcohol-related harm amongst older adults: analysis of existing UK datasets.

Older adults experience age-related physiological changes that increase sensitivity and decrease tolerance to alcohol and there are a number of age-related harms such as falls, social isolation and elder abuse, which are compounded by alcohol misuse. Despite this unique vulnerability and the fact that the number of older adults is increasing, the literature on drinking behaviour and alcohol-related harm in older adults is sparse. This article describes a secondary analysis of UK data to address this knowledge gap

Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in Relativity

Reflections on the labyrinth: Investigating Black and Minority Ethnic leaders’ career experiences

Black and Minority Ethnic (BME) employees appear to experience more difficulty reaching senior leadership positions than their white counterparts. Using Eagly and Carli’s (2007) metaphor of the labyrinth our aim was to give voice to black and minority ethnic managers who have successfully achieved senior management roles, and compare their leadership journeys with those of matched white managers. This paper used semi-structured interviews and attribution theory to examine how 20 black and minority ethnic and 20 white senior managers, from a UK government department made sense of significant career incidents in their leadership journeys. Template analysis was used to identify facilitators and barriers of career progression from causal explanations of these incidents. Although BME and white managers identified four common themes (visibility, networks, development, and line manager support), they differed in how they made sense of formal and informal organisational processes to achieve career progression. The findings are used to theorise about the individual and organisational factors that contribute to the leadership journeys of minority ethnic employees

Physics, Astrophysics and Cosmology with Gravitational Waves

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.Comment: 137 pages, 16 figures, Published version <http://www.livingreviews.org/lrr-2009-2

Phenotypic Variation and Bistable Switching in Bacteria

Microbial research generally focuses on clonal populations. However, bacterial cells with identical genotypes frequently display different phenotypes under identical conditions. This microbial cell individuality is receiving increasing attention in the literature because of its impact on cellular differentiation, survival under selective conditions, and the interaction of pathogens with their hosts. It is becoming clear that stochasticity in gene expression in conjunction with the architecture of the gene network that underlies the cellular processes can generate phenotypic variation. An important regulatory mechanism is the so-called positive feedback, in which a system reinforces its own response, for instance by stimulating the production of an activator. Bistability is an interesting and relevant phenomenon, in which two distinct subpopulations of cells showing discrete levels of gene expression coexist in a single culture. In this chapter, we address techniques and approaches used to establish phenotypic variation, and relate three well-characterized examples of bistability to the molecular mechanisms that govern these processes, with a focus on positive feedback.