Radiation from collapsing shells, semiclassical backreaction and black hole formation

We provide a detailed analysis of quantum field theory around a collapsing shell and discuss several conceptual issues related to the emission of radiation flux and formation of black holes. Explicit calculations are performed using a model for a collapsing shell which turns out to be analytically solvable. We use the insights gained in this model to draw reliable conclusions regarding more realistic models. We first show that any shell of mass $M$ which collapses to a radius close to $r=2M$ will emit approximately thermal radiation for a period of time. In particular, a shell which collapses from some initial radius to a final radius $2M(1-\epsilon^2)^{-1}$ (where $\epsilon \ll 1$) without forming a black hole, will emit thermal radiation during the period $M\lesssim t \lesssim M\ln (1/\epsilon^2)$. Later on ($t\gg M \ln(1/\epsilon^2)$), the flux from such a shell will decay to zero exponentially. We next study the effect of backreaction computed using the vacuum expectation value of the stress tensor on the collapse. We find that, in any realistic collapse scenario, the backreaction effects do \emph{not} prevent the formation of the event horizon. The time at which the event horizon is formed is, of course, delayed due to the radiated flux -- which decreases the mass of the shell -- but this effect is not sufficient to prevent horizon formation. We also clarify several conceptual issues and provide pedagogical details of the calculations in the Appendices to the paper.Comment: 26 pages, 6 figures, revtex4; v2 -- minor reformatting, some typos fixed, one reference added, to appear in PR

A Simple Model for Pulse Profiles from Precessing Pulsars, with Special Application to Relativistic Binary PSR B1913+16

We study the observable pulse profiles that can be generated from precessing pulsars. A novel coordinate system is defined to aid visualization of the observing geometry. Using this system we explore the different families of profiles that can be generated by simple, circularly symmetric beam shapes. An attempt is then made to fit our model to the observations of relativistic binary PSR B1913+16. It is found that while qualitatively similar pulse profiles can be produced, this minimal model is insufficient for an accurate match to the observational data. Consequently, we confirm that the emission beam of PSR B1913+16 must deviate from circular symmetry, as first reported by Weisberg and Taylor. However, the approximate fits obtained suggest that it may be sufficient to consider only minimal deviations from a circular beam in order to explain the data. We also comment on the applicability of our analysis technique to other precessing pulsars, both binary and isolated.Comment: 35 pages and 8 figures. Published versio

High-energy Emission from Pulsar Outer Magnetospheres

We investigate a stationary pair production cascade in the outer magnetosphere of an isolated, spinning neutron star. The charge depletion due to global flows of charged particles, causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate gamma-rays via curvature and inverse-Compton processes. Some of such gamma-rays collide with the X-rays to materialize as pairs in the gap. The replenished charges partially screen the electric field, which is self-consistently solved together with the energy distribution of particles and gamma-rays at each point along the field lines. By solving the set of Maxwell and Boltzmann equations, we demonstrate that an external injection of charged particles at nearly Goldreich-Julian rate does not quench the gap but shifts its position and that the particle energy distribution cannot be described by a power-law. The injected particles are accelerated in the gap and escape from it with large Lorentz factors. We show that such escaping particles migrating outside of the gap contribute significantly to the gamma-ray luminosity for young pulsars and that the soft gamma-ray spectrum between 100 MeV and 3 GeV observed for the Vela pulsar can be explained by this component. We also discuss that the luminosity of the gamma-rays emitted by the escaping particles is naturally proportional to the square root of the spin-down luminosity.Comment: 24 pages, 11 figures; to appear in the inaugural (Sep) issue of Progress in Astrophysics Researches (a new book series

Dynamics of a lattice Universe

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum Gravit

Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable

Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is trace-norm dense in the set of all density operators (and the separable density operators nowhere dense). This result complements recent detailed investigations of separability, which show that when both component Hilbert spaces are finite-dimensional, there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.Comment: 5 pages, RevTe

An appropriate tool for entrepreneurial learning in SMEs? The case of the 20Twenty Leadership Programme

The 20Twenty Leadership Programme was developed by Cardiff Metropolitan University as an executive education programme to be delivered within South Wales to small businesses. It is funded by the European Social Fund (ESF) and administered by the Welsh European Funding Office and has the key aim of developing SME’s growth potential via a range of leadership and management skills, including a focus on ‘soft’ skills. The focus of this paper is to place the 20Twenty Leadership Programme within the wider context of entrepreneurship policy and SME training initiatives in particular, and then to examine the rationale and delivery methods of the Programme in relation to these. It also reflects on the Programme’s success (or otherwise) to date where possible. Finally, the paper seeks to suggest fruitful areas of further research both in terms of the 20Twenty Leadership Programme itself, but also with regard to evaluation in relation to other parallel programmes, and to SME training initiatives more generally

Coaching Stressors in a Division II Historically Black University

Recently, studies have addressed the stressful nature of the coaching profession, identifying a multitude of stressors among coaches for Division I, national, and international programs (Durand-Bush, Collins, & McNeill, 2012; Frey, 2007; Levy, Nicholls, Marchant, & Polman, 2009; Olusoga, Butt, Hays, & Maynard, 2009). The purpose of this study was to further the research by studying coaches at a Historically Black College/University (HBCU) and Division II (DII) athletic program. Participants included seven head and five assistant coaches across seven sports. All coaches were interviewed, based on a preexisting interview guide (Olusoga et al., 2009). Data were content analyzed using previously agreed upon procedures and submitted in NVivo for further examination (Côté, Salmela, Baria, & Russell, 1993). Three higher order themes termed Interpersonal, Intrapersonal, and Contextual Stressors emerged and were composed of 16 lower order themes. The most commonly cited interpersonal stressors included athletes, expectations of others, and administration. Performance outcome and lack of control were the most common intrapersonal stressors. Finally, schedule, lack of resources, and job security were the most common contextual stressors. These findings emphasize the stressful nature of the job and the need to identify means for minimizing stressors to improve the athletic experience for all involved

Local and non-local measures of acceleration in cosmology

Current cosmological observations, when interpreted within the framework of a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) model, strongly suggest that the Universe is entering a period of accelerating expansion. This is often taken to mean that the expansion of space itself is accelerating. In a general spacetime, however, this is not necessarily true. We attempt to clarify this point by considering a handful of local and non-local measures of acceleration in a variety of inhomogeneous cosmological models. Each of the chosen measures corresponds to a theoretical or observational procedure that has previously been used to study acceleration in cosmology, and all measures reduce to the same quantity in the limit of exact spatial homogeneity and isotropy. In statistically homogeneous and isotropic spacetimes, we find that the acceleration inferred from observations of the distance-redshift relation is closely related to the acceleration of the spatially averaged universe, but does not necessarily bear any resemblance to the average of the local acceleration of spacetime itself. For inhomogeneous spacetimes that do not display statistical homogeneity and isotropy, however, we find little correlation between acceleration inferred from observations and the acceleration of the averaged spacetime. This shows that observations made in an inhomogeneous universe can imply acceleration without the existence of dark energy.Comment: 19 pages, 10 figures. Several references added or amended, some minor clarifications made in the tex