Hawking Spectrum and High Frequency Dispersion

We study the spectrum of created particles in two-dimensional black hole geometries for a linear, hermitian scalar field satisfying a Lorentz non-invariant field equation with higher spatial derivative terms that are suppressed by powers of a fundamental momentum scale $k_0$. The preferred frame is the ``free-fall frame" of the black hole. This model is a variation of Unruh's sonic black hole analogy. We find that there are two qualitatively different types of particle production in this model: a thermal Hawking flux generated by ``mode conversion" at the black hole horizon, and a non-thermal spectrum generated via scattering off the background into negative free-fall frequency modes. This second process has nothing to do with black holes and does not occur for the ordinary wave equation because such modes do not propagate outside the horizon with positive Killing frequency. The horizon component of the radiation is astonishingly close to a perfect thermal spectrum: for the smoothest metric studied, with Hawking temperature $T_H\simeq0.0008k_0$, agreement is of order $(T_H/k_0)^3$ at frequency $\omega=T_H$, and agreement to order $T_H/k_0$ persists out to $\omega/T_H\simeq 45$ where the thermal number flux is $O(10^{-20}$). The flux from scattering dominates at large $\omega$ and becomes many orders of magnitude larger than the horizon component for metrics with a ``kink", i.e. a region of high curvature localized on a static worldline outside the horizon. This non-thermal flux amounts to roughly 10\% of the total luminosity for the kinkier metrics considered. The flux exhibits oscillations as a function of frequency which can be explained by interference between the various contributions to the flux.Comment: 32 pages, plain latex, 16 figures included using psfi

Teachers' beliefs about knowledge and learning: A Singapore perspective

The purpose of this study is to explore the complex nature of Singapore teachers' beliefs about knowledge and learning and how these beliefs influence pedagogical practices in their classes. This paper presents findings from a large-scale survey study with 1806 teachers in Singapore. Data revealed that while teachers' beliefs about pedagogies, knowledge and learning were largely consistent, they also believed and practiced both teacher-centered and learner-centered pedagogies and assessment methods

Phenomenological covariant approach to gravity

We covariantly modify the Einstein-Hilbert action such that the modified action perturbatively resolves the flat rotational velocity curve of the spiral galaxies and gives rise to the Tully-Fisher relation, and dynamically generates the cosmological constant. This modification requires introducing just a single new universal parameter.Comment: v6: a mistake in deriving the equation of the cosmological constant corrected, refs adde

Gravitational Duality in MacDowell-Mansouri Gauge Theory

Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show that an analogous procedure allows to find the dual action to the gauge theory of gravity constructed by the MacDowell-Mansouri model plus the superposition of a $\Theta$ term.Comment: 9 pages, LaTeX, no figure

Black Hole Evaporation in the Presence of a Short Distance Cutoff

A derivation of the Hawking effect is given which avoids reference to field modes above some cutoff frequency $\omega_c\gg M^{-1}$ in the free-fall frame of the black hole. To avoid reference to arbitrarily high frequencies, it is necessary to impose a boundary condition on the quantum field in a timelike region near the horizon, rather than on a (spacelike) Cauchy surface either outside the horizon or at early times before the horizon forms. Due to the nature of the horizon as an infinite redshift surface, the correct boundary condition at late times outside the horizon cannot be deduced, within the confines of a theory that applies only below the cutoff, from initial conditions prior to the formation of the hole. A boundary condition is formulated which leads to the Hawking effect in a cutoff theory. It is argued that it is possible the boundary condition is {\it not} satisfied, so that the spectrum of black hole radiation may be significantly different from that predicted by Hawking, even without the back-reaction near the horizon becoming of order unity relative to the curvature.Comment: 35 pages, plain LaTeX, UMDGR93-32, NSF-ITP-93-2

Quantum limits on phase-shift detection using multimode interferometers

Fundamental phase-shift detection properties of optical multimode interferometers are analyzed. Limits on perfectly distinguishable phase shifts are derived for general quantum states of a given average energy. In contrast to earlier work, the limits are found to be independent of the number of interfering modes. However, the reported bounds are consistent with the Heisenberg limit. A short discussion on the concept of well-defined relative phase is also included.Comment: 6 pages, 3 figures, REVTeX, uses epsf.st

Focusing and the Holographic Hypothesis

The ``screen mapping" introduced by Susskind to implement 't Hooft's holographic hypothesis is studied. For a single screen time, there are an infinite number of images of a black hole event horizon, almost all of which have smaller area on the screen than the horizon area. This is consistent with the focusing equation because of the existence of focal points. However, the {\it boundary} of the past (or future) of the screen obeys the area theorem, and so always gives an expanding map to the screen, as required by the holographic hypothesis. These considerations are illustrated with several axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi

Modified Gravity via Spontaneous Symmetry Breaking

We construct effective field theories in which gravity is modified via spontaneous breaking of local Lorentz invariance. This is a gravitational analogue of the Higgs mechanism. These theories possess additional graviton modes and modified dispersion relations. They are manifestly well-behaved in the UV and free of discontinuities of the van Dam-Veltman-Zakharov type, ensuring compatibility with standard tests of gravity. They may have important phenomenological effects on large distance scales, offering an alternative to dark energy. For the case in which the symmetry is broken by a vector field with the wrong sign mass term, we identify four massless graviton modes (all with positive-definite norm for a suitable choice of a parameter) and show the absence of the discontinuity.Comment: 5 pages; revised versio

The BEST study - a prospective study to compare business class versus economy class air travel as a cause of thrombosis

Background. As many as 10% of airline passengers travelling without prophylaxis for long distances may develop a venous thrombosis. There is, however, no evidence that economy class travellers are at increased risk of thrombosis.Objectives. A suitably powered prospective study, based on the incidence of deep-vein thrombosis (DVT) reported in previous studies on long-haul flights, was designed to determine the incidence of positive venous duplex scans and D-dimer elevations in low and intermediate-risk passengers, comparing passengers travelling in business and economy class.Patients/methods. Eight hundred and ninety-nine passengers were recruited (180 travelling business class and 719 travelling economy). D-dimers were measured before and after the flight. A value greater than 500 ng/ml was accepted as abnormal. A thrombophilia screen was conducted which included the factor V Leiden mutation, the prothombin 20210A mutation, protein C and S levels, antithrombin levels, and anticardiolipin antibodies immunoglobulin G (IgG) and immunoglobulin M (IgM). On arrival, lower limb compression ultrasonography of the deep veins was performed. Logistical regression analysis was used to determine the risk factors related to abnormally high D-dimer levels.Results. Only 434 subjects had a full venous duplex scan performed. None had ultrasonic evidence of venous thrombosis. Nine passengers tested at departure had elevated D-dimer levels and these volunteers were excluded from further study. Seventy-four of the 899 passengers had raised D-dimers on arrival. Twenty-two of 180 business class passengers (12%) developed elevated D-dimers compared with 52 of 719 economy class passengers (7%). There was no significant association between elevation of D-dimers and the class flown (odds ratio (OR) 0.61, p = 0.109). The factor V Leiden mutation, factor VIII levels and the use of aspirin were, however, associated with raised D-dimers (OR 3.36, p = 0.024; OR 1.01, p = 0.014; and OR 2.04, p = 0.038, respectively). Five hundred and five passengers were contacted within 6 months and none reported any symptoms of a clinical thrombosis or pulmonary embolus.Conclusion. The incidence of ultrasonically proven DVT is much lower than previously reported. However, more than 10% of all passengers developed raised D-dimers, which were unrelated to the class flown. A rise in D-dimers is associated with an inherent risk of thrombosis and/ or thrombophilia, demonstrates activation of both the coagulation and fibrinolytic systems during long-haul flights, and may indicate the development of small thrombi

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page