Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres

In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds, that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case where both are equal to two, where existence of non-negatively curved metrics is known.Comment: 10 page

The ^(54)Mn Clock and Its Implications for Cosmic Ray Propagation and Fe Isotope Studies

Radioactive ^(54)Mn suggested as a 'clock' for measuring the lifetime of heavy cosmic rays, has a poorly known β-decay half-life estimated to be in the range from ~10^5 to 10 ^7 yr. Some years ago Koch et al. concluded from measurements of the Mn/Fe ratio that a significant fraction of low-energy (<1 GeV/nucleon) ^(54)Mn produced by Fe fragmentation had decayed. Using a propagation code that includes improved fragmentation cross-sections, and recent data from HEAO 3 and a number of other spacecraft, we have reexamined the evidence for ^(54)Mn decay in cosmic rays. We conclude that present cosmic-ray data cannot establish the degree of ^(54)Mn decay, but point out that this question has important implications for studies of the ^(54)Fe abundance in cosmic-ray source material, as well as for cosmic-ray propagation studies

Radiation from a uniformly accelerating harmonic oscillator

We consider a radiation from a uniformly accelerating harmonic oscillator whose minimal coupling to the scalar field changes suddenly. The exact time evolutions of the quantum operators are given in terms of a classical solution of a forced harmonic oscillator. After the jumping of the coupling constant there occurs a fast absorption of energy into the oscillator, and then a slow emission follows. Here the absorbed energy is independent of the acceleration and proportional to the log of a high momentum cutoff of the field. The emitted energy depends on the acceleration and also proportional to the log of the cutoff. Especially, if the coupling is comparable to the natural frequency of the detector ($e^2/(4m) \sim \omega_0$) enormous energies are radiated away from the oscillator.Comment: 26 pages, 1 eps figure, RevTeX, minor correction in grammar, add a discussio

Modern technologies of adaptation young specialists in the organization

In this article the main directions and technologies of adaptation of young specialists are considered. The author has revealed new technology of adaptation of young specialists which will allow new employees to feel more comfortably on a new workplace, to join collective, and also will lead to reduction of a dissatisfaction and turnover of staff at an initial stage of adaptation

The Rotating Quantum Vacuum

We derive conditions for rotating particle detectors to respond in a variety of bounded spacetimes and compare the results with the folklore that particle detectors do not respond in the vacuum state appropriate to their motion. Applications involving possible violations of the second law of thermodynamics are briefly addressed.Comment: Plain TeX, 10 pages (to appear in PRD

The Energy-Momentum Tensor in Fulling-Rindler Vacuum

The energy density in Fulling-Rindler vacuum, which is known to be negative "everywhere" is shown to be positive and singular on the horizons in such a fashion as to guarantee the positivity of the total energy. The mechanism of compensation is displayed in detail.Comment: 9 pages, ULB-TH-15/9

The Singularity Problem for Space-Times with Torsion

The problem of a rigorous theory of singularities in space-times with torsion is addressed. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors have done, because their definition of geodesics only involves the Christoffel connection, though studying theories with torsion. We propose a preliminary definition of singularities which is based on timelike or null geodesic incompleteness, even though for theories with torsion the paths of particles are not geodesics. The study of the geodesic equation for cosmological models with torsion shows that the definition has a physical relevance. It can also be motivated, as done in the literature, remarking that the causal structure of a space-time with torsion does not get changed with respect to general relativity. We then prove how to extend Hawking's singularity theorem without causality assumptions to the space-time of the ECSK theory. This is achieved studying the generalized Raychaudhuri equation in the ECSK theory, the conditions for the existence of conjugate points and properties of maximal timelike geodesics. Hawking's theorem can be generalized, provided the torsion tensor obeys some conditions. Thus our result can also be interpreted as a no-singularity theorem if these additional conditions are not satisfied. In other words, it turns out that the occurrence of singularities in closed cosmological models based on the ECSK theory is less generic than in general relativity. Our work is to be compared with previous papers in the literature. There are some relevant differences, because we rely on a different definition of geodesics, we keep the field equations of the ECSK theory in their original form rather than casting them in a form similar to general relativity with a modified energy momentum tensor,Comment: 17 pages, plain-tex, published in Nuovo Cimento B, volume 105, pages 75-90, year 199

Prospectus, December 12, 1972

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Nonthermal nature of incipient extremal black holes

We examine particle production from spherical bodies collapsing into extremal Reissner-Nordstr\"om black holes. Kruskal coordinates become ill-defined in the extremal case, but we are able to find a simple generalization of them that is good in this limit. The extension allows us to calculate the late-time worldline of the center of the collapsing star, thus establishing a correspondence with a uniformly accelerated mirror in Minkowski spacetime. The spectrum of created particles associated with such uniform acceleration is nonthermal, indicating that a temperature is not defined. Moreover, the spectrum contains a constant that depends on the history of the collapsing object. At first sight this points to a violation of the no-hair theorems; however, the expectation value of the stress-energy-momentum tensor is zero and its variance vanishes as a power law at late times. Hence, both the no-hair theorems and the cosmic censorship conjecture are preserved. The power-law decay of the variance is in distinction to the exponential fall-off of a nonextremal black hole. Therefore, although the vanishing of the stress tensor's expectation value is consistent with a thermal state at zero temperature, the incipient black hole does not behave as a thermal object at any time and cannot be regarded as the thermodynamic limit of a nonextremal black hole, regardless of the fact that the final product of collapse is quiescent.Comment: 13 pages, 2 epsf figures, RevTeX 3. Minor changes, version published in PR