New representation and a vacuum state for canonical quantum gravity

A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal state functional can be given, which has some typical features of a vacuum state in quantum field theory. It can be canonically transformed into the metric representation. Transforming the constraints too, one recovers the Wheeler~DeWitt equation up to an anomalous term. A modified Dirac quantization is proposed to handle possible anomalies in the constraint algebra.Comment: 28 pages, LaTe

String dynamics and ejection along the axis of a spinning black hole

Relativistic current carrying strings moving axisymmetrically on the background of a Kerr black hole are studied. The boundaries and possible types of motion of a string with a given energy and current are found. Regions of parameters for which the string falls into the black hole, or is trapped in a toroidal volume, or can escape to infinity, are identified, and representative trajectories are examined by numerical integration, illustrating various interesting behaviors. In particular, we find that a string can start out at rest near the equatorial plane and, after bouncing around, be ejected out along the axis, some of its internal (elastic or rotational kinetic) energy having been transformed into translational kinetic energy. The resulting velocity can be an order unity fraction of the speed of light. This process results from the presence of an outer tension barrier and an inner angular momentum barrier that are deformed by the gravitational field. We speculatively discuss the possible astrophysical significance of this mechanism as a means of launching a collimated jet of MHD plasma flux tubes along the spin axis of a gravitating system fed by an accretion disk.Comment: 14 pages, 11 figures; v.2: minor edits, references added, typos corrected, published versio

Comment on "Accelerated Detectors and Temperature in (Anti) de Sitter Spaces"

It is shown how the results of Deser and Levin on the response of accelerated detectors in anti-de Sitter space can be understood from the same general perspective as other thermality results in spacetimes with bifurcate Killing horizons.Comment: 5 pages, LaTe

Relativistic Acoustic Geometry

Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field propagating in a curved space-time geometry. The geometry is described by the acoustic metric tensor that depends locally on the equation of state and the four-velocity of the fluid. For a relativistic supersonic flow in curved space-time the ergosphere and acoustic horizon may be defined in a way analogous the non-relativistic case. A general-relativistic expression for the acoustic analog of surface gravity has been found.Comment: 14 pages, LaTe

Probing Fine-Scale Ionospheric Structure with the Very Large Array Radio Telescope

High resolution (~1 arcminute) astronomical imaging at low frequency (below 150 MHz) has only recently become practical with the development of new calibration algorithms for removing ionospheric distortions. In addition to opening a new window in observational astronomy, the process of calibrating the ionospheric distortions also probes ionospheric structure in an unprecedented way. Here we explore one aspect of this new type of ionospheric measurement, the differential refraction of celestial source pairs as a function of their angular separation. This measurement probes variations in the spatial gradient of the line-of-sight total electron content (TEC) to 0.001 TECU/km accuracy over spatial scales of under 10 km to over 100 km. We use data from the VLA Low-frequency Sky Survey (VLSS; Cohen et al. 2007, AJ 134, 1245), a nearly complete 74 MHz survey of the entire sky visible to the Very Large Array (VLA) telescope in Socorro, New Mexico. These data comprise over 500 hours of observations, all calibrated in a standard way. While ionospheric spatial structure varies greatly from one observation to the next, when analyzed over hundreds of hours, statistical patterns become apparent. We present a detailed characterization of how the median differential refraction depends on source pair separation, elevation and time of day. We find that elevation effects are large, but geometrically predictable and can be "removed" analytically using a "thin-shell" model of the ionosphere. We find significantly greater ionospheric spatial variations during the day than at night. These diurnal variations appear to affect the larger angular scales to a greater degree indicating that they come from disturbances on relatively larger spatial scales (100s of km, rather than 10s of km).Comment: Accepted for publication by The Astronomical Journa

Degenerate Sectors of the Ashtekar Gravity

This work completes the task of solving locally the Einstein-Ashtekar equations for degenerate data. The two remaining degenerate sectors of the classical 3+1 dimensional theory are considered. First, with all densitized triad vectors linearly dependent and second, with only two independent ones. It is shown how to solve the Einstein-Ashtekar equations completely by suitable gauge fixing and choice of coordinates. Remarkably, the Hamiltonian weakly Poisson commutes with the conditions defining the sectors. The summary of degenerate solutions is given in the Appendix.Comment: 19 pages, late

Octonions, E6, and Particle Physics

In 1934, Jordan et al. gave a necessary algebraic condition, the Jordan identity, for a sensible theory of quantum mechanics. All but one of the algebras that satisfy this condition can be described by Hermitian matrices over the complexes or quaternions. The remaining, exceptional Jordan algebra can be described by 3x3 Hermitian matrices over the octonions. We first review properties of the octonions and the exceptional Jordan algebra, including our previous work on the octonionic Jordan eigenvalue problem. We then examine a particular real, noncompact form of the Lie group E6, which preserves determinants in the exceptional Jordan algebra. Finally, we describe a possible symmetry-breaking scenario within E6: first choose one of the octonionic directions to be special, then choose one of the 2x2 submatrices inside the 3x3 matrices to be special. Making only these two choices, we are able to describe many properties of leptons in a natural way. We further speculate on the ways in which quarks might be similarly encoded.Comment: 13 pages; 6 figures; TonyFest plenary talk (York 2008

A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra

A study of the set N_p of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p>0 was initiated by Shalev and continued by the present author. The main goal of this paper is to show the abundance of elements of N_p. Our main result shows that any divisor n of q-1, where q is a power of p, such that $n\ge (p-1)^{1/p} (q-1)^{1-1/(2p)}$, belongs to N_p. This extends its special case for p=2 which was proved in a previous paper by a different method.Comment: 10 pages. This version has been revised according to a referee's suggestions. The additions include a discussion of the (lower) density of the set N_p, and the results of more extensive machine computations. Note that the title has also changed. To appear in Israel J. Mat

Evaluation of positive G sub Z tolerance following simulated weightlessness (bedrest)

The magnitude of physiologic changes which are known to occur in human subjects exposed to varying levels of + G sub Z acceleration following bed rest simulation of weightlessness was studied. Bed rest effects were documented by fluid and electrolyte balance studies, maximal exercise capability, 70 deg passive tilt and lower body negative pressure tests and the ability to endure randomly prescribed acceleration profiles of +2G sub Z, +3G sub Z, and +4G sub Z. Six healthy male volunteers were studied during two weeks of bed rest after adequate control observations, followed by two weeks of recovery, followed by a second two-week period of bed rest at which time an Air Force cutaway anti-G suit was used to determine its effectiveness as a countermeasure for observed cardiovascular changes during acceleration. Results showed uniform and significant changes in all measured parameters as a consequence of bed rest including a reduced ability to tolerate +G sub Z acceleration. The use of anti-G suits significantly improved subject tolerance to all G exposures and returned measured parameters such as heart rate and blood pressure towards or to pre-bed-rest (control) values in four of the six cases

Minimal Off-Shell Version of N = 1 Chiral Supergravity

We construct the minimal off-shell formulation of N = 1 chiral supergravity (SUGRA) introducing a complex antisymmetric tensor field $B_{\mu \nu}$ and a complex axial-vector field $A_{\mu}$ as auxiliary fields. The resulting algebra of the right- and left-handed supersymmetry (SUSY) transformations closes off shell and generates chiral gauge transforamtions and vector gauge transformations in addition to the transformations which appear in the case without auxiliary fields.Comment: 9 pages, late