Degeneracy measures for the algebraic classification of numerical spacetimes

We study the issue of algebraic classification of the Weyl curvature tensor, with a particular focus on numerical relativity simulations. The spacetimes of interest in this context, binary black hole mergers, and the ringdowns that follow them, present subtleties in that they are generically, strictly speaking, Type I, but in many regions approximately, in some sense, Type D. To provide meaning to any claims of "approximate" Petrov class, one must define a measure of degeneracy on the space of null rays at a point. We will investigate such a measure, used recently to argue that certain binary black hole merger simulations ring down to the Kerr geometry, after hanging up for some time in Petrov Type II. In particular, we argue that this hangup in Petrov Type II is an artefact of the particular measure being used, and that a geometrically better-motivated measure shows a black hole merger produced by our group settling directly to Petrov Type D.Comment: 14 pages, 7 figures. Version 2 adds two references

Computational Efficiency of Frequency-- and Time--Domain Calculations of Extreme Mass--Ratio Binaries: Equatorial Orbits

Gravitational waveforms and fluxes from extreme mass--ratio inspirals can be computed using time--domain methods with accuracy that is fast approaching that of frequency--domain methods. We study in detail the computational efficiency of these methods for equatorial orbits of fast spinning Kerr black holes, and find the number of modes needed in either method --as functions of the orbital parameters-- in order to achieve a desired accuracy level. We then estimate the total computation time and argue that for high eccentricity orbits the time--domain approach is more efficient computationally. We suggest that in practice low--$m$ modes are computed using the frequency--domain approach, and high--$m$ modes are computed using the time--domain approach, where $m$ is the azimuthal mode number.Comment: 19 figures, 6 table

Curvature invariants in type N spacetimes

Scalar curvature invariants are studied in type N solutions of vacuum Einstein's equations with in general non-vanishing cosmological constant Lambda. Zero-order invariants which include only the metric and Weyl (Riemann) tensor either vanish, or are constants depending on Lambda. Even all higher-order invariants containing covariant derivatives of the Weyl (Riemann) tensor are shown to be trivial if a type N spacetime admits a non-expanding and non-twisting null geodesic congruence. However, in the case of expanding type N spacetimes we discover a non-vanishing scalar invariant which is quartic in the second derivatives of the Riemann tensor. We use this invariant to demonstrate that both linearized and the third order type N twisting solutions recently discussed in literature contain singularities at large distances and thus cannot describe radiation fields outside bounded sources.Comment: 17 pages, to appear in Class. Quantum Gra

Understanding social and clinical associations with unemployment for people with schizophrenia and bipolar disorders: large-scale health records study

Purpose People with severe mental illness (SMI) experience high levels of unemployment. We aimed to better understand the associations between clinical, social, and demographic inequality indicators and unemployment. Methods Data were extracted from de-identified health records of people with SMI in contact with secondary mental health services in south London, UK. A Natural Language Processing text-mining application was applied to extract information on unemployment in the health records. Multivariable logistic regression was used to assess associations with unemployment, in people with SMI. Results Records from 19,768 service users were used for analysis, 84.9% (n = 16,778) had experienced unemployment. In fully adjusted models, Black Caribbean and Black African service users were more likely to experience unemployment compared with White British service users (Black Caribbean: aOR 1.62, 95% CI 1.45–1.80; Black African: 1.32, 1.15–1.51). Although men were more likely to have experienced unemployment relative to women in unadjusted models (OR 1.36, 95% CI 1.26–1.47), differences were no longer apparent in the fully adjusted models (aOR 1.05, 95% CI 0.97–1.15). The presence of a non-affective (compared to affective) diagnosis (1.24, 1.13–1.35), comorbid substance use (2.02, 1.76–2.33), previous inpatient admissions (4.18, 3.71–4.70), longer inpatient stays (78 + days: 7.78, 6.34–9.54), and compulsory admissions (3.45, 3.04–3.92) were associated with unemployment, in fully adjusted models. Conclusion People with SMI experience high levels of unemployment, and we found that unemployment was associated with several clinical and social factors. Interventions to address low employment may need to also address these broader inequalities

On asymptotically flat solutions of Einstein's equations periodic in time I. Vacuum and electrovacuum solutions

By an argument similar to that of Gibbons and Stewart, but in a different coordinate system and less restrictive gauge, we show that any weakly-asymptotically-simple, analytic vacuum or electrovacuum solutions of the Einstein equations which are periodic in time are necessarily stationary.Comment: 25 pages, 2 figures, published in Class. Quant. Grav

Gauge-invariant magnetic perturbations in perfect-fluid cosmologies

We develop further our extension of the Ellis-Bruni covariant and gauge-invariant formalism to the general relativistic treatment of density perturbations in the presence of cosmological magnetic fields. We present detailed analysis of the kinematical and dynamical behaviour of perturbed magnetized FRW cosmologies containing fluid with non-zero pressure. We study the magnetohydrodynamical effects on the growth of density irregularities during the radiation era. Solutions are found for the evolution of density inhomogeneities on small and large scales in the presence of pressure, and some new physical effects are identified.Comment: Revised version (some minor changes - few equations added). 26 pages. No figures. To appear in Classical and Quantum Gravit

Boost-rotation symmetric type D radiative metrics in Bondi coordinates

The asymptotic properties of the solutions to the Einstein-Maxwell equations with boost-rotation symmetry and Petrov type D are studied. We find series solutions to the pertinent set of equations which are suitable for a late time descriptions in coordinates which are well adapted for the description of the radiative properties of spacetimes (Bondi coordinates). By calculating the total charge, Bondi and NUT mass and the Newman-Penrose constants of the spacetimes we provide a physical interpretation of the free parameters of the solutions. Additional relevant aspects on the asymptotics and radiative properties of the spacetimes considered, such as the possible polarization states of the gravitational and electromagnetic field, are discussed through the way

Bianchi type II,III and V diagonal Einstein metrics re-visited

We present, for both minkowskian and euclidean signatures, short derivations of the diagonal Einstein metrics for Bianchi type II, III and V. For the first two cases we show the integrability of the geodesic flow while for the third case a somewhat unusual bifurcation phenomenon takes place: for minkowskian signature elliptic functions are essential in the metric while for euclidean signature only elementary functions appear

Identifying socio-demographic and socioeconomic determinants of health inequalities in a diverse London community: the South East London Community Health (SELCoH) study

<p>Abstract</p> <p>Background</p> <p>Responses to public health need require information on the distribution of mental and physical ill health by demographic and socioeconomic factors at the local community level.</p> <p>Methods</p> <p>The South East London Community Health (SELCoH) study is a community psychiatric and physical morbidity survey. Trained interviewers conducted face-to-face computer assisted interviews with 1698 adults aged 16 years and over, from 1076 randomly selected private households in two south London boroughs. We compared the prevalence of common mental disorders, hazardous alcohol use, long standing illness and general physical health by demographic and socioeconomic indicators. Unadjusted and models adjusted for demographic and socioeconomic indicators are presented for all logistic regression models.</p> <p>Results</p> <p>Of those in the sample, 24.2% reported common mental disorder and 44.9% reported having a long standing illness, with 15.7% reporting hazardous alcohol consumption and 19.2% rating their health as fair or poor. The pattern of indicators identifying health inequalities for common mental disorder, poor general health and having a long term illness is similar; individuals who are socioeconomically disadvantaged have poorer health and physical health worsens as age increases for all groups. The prevalence of poor health outcomes by ethnic group suggests that there are important differences between groups, particularly for common mental disorder and poor general health. Higher socioeconomic status was protective for common mental disorder, fair or poor health and long standing illness, but those with higher socioeconomic status reported higher levels of hazardous alcohol use. The proportion of participants who met the criteria for common mental disorder with co-occurring functional limitations was similar or greater to those with poor physical health.</p> <p>Conclusions</p> <p>Health service providers and policy makers should prioritise high risk, socially defined groups in combating inequalities in individual and co-occurring poor mental and physical problems. In population terms, poor mental health has a similar or greater burden on functional impairment than long term conditions and perceived health.</p

Collisional equilibrium, particle production and the inflationary universe

Particle production processes in the expanding universe are described within a simple kinetic model. The equilibrium conditions for a Maxwell-Boltzmann gas with variable particle number are investigated. We find that radiation and nonrelativistic matter may be in equilibrium at the same temperature provided the matter particles are created at a rate that is half the expansion rate. Using the fact that the creation of particles is dynamically equivalent to a nonvanishing bulk pressure we calculate the backreaction of this process on the cosmological dynamics. It turns out that the `adiabatic' creation of massive particles with an equilibrium distribution for the latter necessarily implies power-law inflation. Exponential inflation in this context is shown to become inconsistent with the second law of thermodynamics after a time interval of the order of the Hubble time.Comment: 19 pages, latex, no figures, to appear in Phys.Rev.