A Note on the Instability of Lorentzian Taub-NUT-Space

I show that there are no SU(2)-invariant (time-dependent) tensorial perturbations of Lorentzian Taub-NUT space. It follows that the spacetime is unstable at the linear level against generic perturbations. I speculate that this fact is responsible for so far unsuccessful attempts to define a sensible thermodynamics for NUT-charged spacetimes.Comment: 13 pages, no figure

On asymptotically flat solutions of Einstein's equations periodic in time II. Spacetimes with scalar-field sources

We extend the work in our earlier article [4] to show that time-periodic, asymptotically-flat solutions of the Einstein equations analytic at scri, whose source is one of a range of scalar-field models, are necessarily stationary. We also show that, for some of these scalar-field sources, in stationary, asymptotically-flat solutions analytic at scri, the scalar field necessarily inherits the symmetry. To prove these results we investigate miscellaneous properties of massless and conformal scalar fields coupled to gravity, in particular Bondi mass and its loss.Comment: 29 pages, published in Class. Quant. Grav. Replaced. Typos corrected, version which appeared in Class. Quant.Gra

The Measure Problem in Cosmology

The Hamiltonian structure of general relativity provides a natural canonical measure on the space of all classical universes, i.e., the multiverse. We review this construction and show how one can visualize the measure in terms of a "magnetic flux" of solutions through phase space. Previous studies identified a divergence in the measure, which we observe to be due to the dilatation invariance of flat FRW universes. We show that the divergence is removed if we identify universes which are so flat they cannot be observationally distinguished. The resulting measure is independent of time and of the choice of coordinates on the space of fields. We further show that, for some quantities of interest, the measure is very insensitive to the details of how the identification is made. One such quantity is the probability of inflation in simple scalar field models. We find that, according to our implementation of the canonical measure, the probability for N e-folds of inflation in single-field, slow-roll models is suppressed by of order exp(-3N) and we discuss the implications of this result.Comment: 22 pages, 6 figures. Revised version with clarifying remarks on meaning of adopted measure, extra references and minor typographical correction

Classical and Quantum Analysis of Repulsive Singularities in Four Dimensional Extended Supergravity

Non--minimal repulsive singularities (``repulsons'') in extended supergravity theories are investigated. The short distance antigravity properties of the repulsons are tested at the classical and the quantum level by a scalar test--particle. Using a partial wave expansion it is shown that the particle gets totally reflected at the origin. A high frequency incoming particle undergoes a phase shift of $\frac{\pi}{2}$. However, the phase shift for a low--frequency particle depends upon the physical data of the repulson. The curvature singularity at a finite distance $r_h$ turns out to be transparent for the scalar test--particle and the coordinate singularity at the origin serves as a repulsive barrier at which particles bounce off.Comment: 20 pages, 14 figure

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

Global embedding of the Kerr black hole event horizon into hyperbolic 3-space

An explicit global and unique isometric embedding into hyperbolic 3-space, H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H^3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event horizon into H^3, for arbitrary values of the angular momentum. For this example, considering a quotient of H^3 by the Picard group, we show that the hyperbolic embedding fits in a fundamental domain of the group up to a slightly larger value of the angular momentum than the limit for which a global embedding into Euclidean 3-space is possible. An embedding of the double-Kerr event horizon is also presented, as an example of an embedding which cannot be made global.Comment: 16 pages, 13 figure

Axially Symmetric Bianchi I Yang-Mills Cosmology as a Dynamical System

We construct the most general form of axially symmetric SU(2)-Yang-Mills fields in Bianchi cosmologies. The dynamical evolution of axially symmetric YM fields in Bianchi I model is compared with the dynamical evolution of the electromagnetic field in Bianchi I and the fully isotropic YM field in Friedmann-Robertson-Walker cosmologies. The stochastic properties of axially symmetric Bianchi I-Einstein-Yang-Mills systems are compared with those of axially symmetric YM fields in flat space. After numerical computation of Liapunov exponents in synchronous (cosmological) time, it is shown that the Bianchi I-EYM system has milder stochastic properties than the corresponding flat YM system. The Liapunov exponent is non-vanishing in conformal time.Comment: 18 pages, 6 Postscript figures, uses amsmath,amssymb,epsfig,verbatim, to appear in CQ

Prevalence and Predictors of Abnormal Cardiovascular Responses to Exercise Testing Among Individuals With Type 2 Diabetes: The Look AHEAD (Action for Health in Diabetes) study

OBJECTIVE We examined maximal graded exercise test (GXT) results in 5,783 overweight/obese men and women, aged 45–76 years, with type 2 diabetes, who were entering the Look AHEAD (Action for Health in Diabetes) study, to determine the prevalence and correlates of exercise-induced cardiac abnormalities. RESEARCH DESIGN AND METHODS Participants underwent symptom-limited maximal GXTs. Questionnaires and physical examinations were used to determine demographic, anthropometric, metabolic, and health status predictors of abnormal GXT results, which were defined as an ST segment depression ≥1.0 mm, ventricular arrhythmia, angina pectoris, poor postexercise heart rate recovery (<22 bpm reduction 2 min after exercise), or maximal exercise capacity less than 5.0 METs. Systolic blood pressure response to exercise was examined as a continuous variable, without a threshold to define abnormality. RESULTS Exercise-induced abnormalities were present in 1,303 (22.5%) participants, of which 693 (12.0%) consisted of impaired exercise capacity. ST segment depression occurred in 440 (7.6%), abnormal heart rate recovery in 206 (5.0%), angina in 63 (1.1%), and arrhythmia in 41 (0.7%). Of potential predictors, only greater age was associated with increased prevalence of all abnormalities. Other predictors were associated with some, but not all, abnormalities. Systolic blood pressure response decreased with greater age, duration of diabetes, and history of cardiovascular disease. CONCLUSIONS We found a high rate of abnormal GXT results despite careful screening for cardiovascular disease symptoms. In this cohort of overweight and obese individuals with type 2 diabetes, greater age most consistently predicted abnormal GXT. Long-term follow-up of these participants will show whether these abnormalities are clinically significant. Cardiovascular disease (CVD) risk factors improve with exercise in individuals with diabetes (1). Similarly, individuals with diabetes who are physically active or have higher fitness levels have reduced CVD incidence and mortality (2,3). Nevertheless, participation in exercise may involve risks for individuals with diabetes because of their high prevalence of CVD, including silent ischemia, and other comorbid conditions (4). Knowledge about the typical cardiovascular responses to exercise in individuals with type 2 diabetes has come mainly from small clinic-based studies (5) and a few larger studies in the general population (4,6,7). The Look AHEAD (Action for Health in Diabetes) study is a multicenter randomized clinical trial designed to evaluate the long-term effects of an intensive lifestyle intervention program of weight loss and physical activity on morbidity and mortality from CVD in overweight and obese individuals with type 2 diabetes (8). Graded exercise tests (GXTs) with electrocardiographic monitoring were conducted at baseline in 5,783 individuals, providing the largest sample of systematic stress testing ever conducted in individuals with type 2 diabetes. The aims of this analysis are to examine the range of abnormal exercise responses and to examine the degree to which demographic factors, health characteristics, and medication use associate with abnormal exercise responses. Identifying predictors from readily available demographic and clinical data may assist risk stratification before exercise testing or exercise prescription for individuals with diabetes

A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models

Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently regained interest as a good fit to the observed cosmic microwave background temperature fluctuations. However, it is generally thought that a globally, exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a probability space on the set F of compact, comoving, 3-spatial sections of FLRW models, a physically motivated hypothesis is proposed, using the density parameter Omega as a derived rather than fundamental parameter. We assume that the processes that select the 3-manifold also select a global mass-energy and a Hubble parameter. The inferred range in Omega consists of a single real value for any 3-manifold. Thus, the obvious measure over F is the discrete measure. Hence, if the global mass-energy and Hubble parameter are a function of 3-manifold choice among compact FLRW models, then probability spaces parametrised by Omega do not, in general, give a zero probability of a flat model. Alternatively, parametrisation by the injectivity radius r_inj ("size") suggests the Lebesgue measure. In this case, the probability space over the injectivity radius implies that flat models occur almost surely (a.s.), in the sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3: generalisation: m, H functions of

Isolated Horizons: Hamiltonian Evolution and the First Law

A framework was recently introduced to generalize black hole mechanics by replacing stationary event horizons with isolated horizons. That framework is significantly extended. The extension is non-trivial in that not only do the boundary conditions now allow the horizon to be distorted and rotating, but also the subsequent analysis is based on several new ingredients. Specifically, although the overall strategy is closely related to that in the previous work, the dynamical variables, the action principle and the Hamiltonian framework are all quite different. More importantly, in the non-rotating case, the first law is shown to arise as a necessary and sufficient condition for the existence of a consistent Hamiltonian evolution. Somewhat surprisingly, this consistency condition in turn leads to new predictions even for static black holes. To complement the previous work, the entire discussion is presented in terms of tetrads and associated (real) Lorentz connections.Comment: 56 pages, 1 figure, Revtex; Final Version, to appear in PR