Symmetric hyperbolic systems for a large class of fields in arbitrary dimension

Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance of the so-called "superenergy" tensors, which provide the necessary symmetric positive matrices, is emphasized and made explicit. Thereby, a unified treatment of many physical systems is achieved, as well as of the sometimes called "higher order" systems. The characteristics of these symmetric hyperbolic systems are always physical, and directly related to the null directions of the superenergy tensor, which are in particular principal null directions of the tensor field solutions. Generic energy estimates and inequalities are presented too.Comment: 24 pages, no figure

Fast rotating stars resulting from binary evolution will often appear to be single

Rapidly rotating stars are readily produced in binary systems. An accreting star in a binary system can be spun up by mass accretion and quickly approach the break-up limit. Mergers between two stars in a binary are expected to result in massive, fast rotating stars. These rapid rotators may appear as Be or Oe stars or at low metallicity they may be progenitors of long gamma-ray bursts. Given the high frequency of massive stars in close binaries it seems likely that a large fraction of rapidly rotating stars result from binary interaction. It is not straightforward to distinguish a a fast rotator that was born as a rapidly rotating single star from a fast rotator that resulted from some kind of binary interaction. Rapidly rotating stars resulting from binary interaction will often appear to be single because the companion tends to be a low mass, low luminosity star in a wide orbit. Alternatively, they became single stars after a merger or disruption of the binary system during the supernova explosion of the primary. The absence of evidence for a companion does not guarantee that the system did not experience binary interaction in the past. If binary interaction is one of the main causes of high stellar rotation rates, the binary fraction is expected to be smaller among fast rotators. How this prediction depend on uncertainties in the physics of the binary interactions requires further investigation.Comment: 2 pages, 1 figure, to be published in the proceedings of IAU 272 "Active OB stars: structure, evolution, mass loss and critical limit", Paris 19-23 July 201

Quantization of the Maxwell field in curved spacetimes of arbitrary dimension

We quantize the massless p-form field that obeys the generalized Maxwell field equations in curved spacetimes of dimension n > 1. We begin by showing that the classical Cauchy problem of the generalized Maxwell field is well posed and that the field possess the expected gauge invariance. Then the classical phase space is developed in terms of gauge equivalent classes, first in terms of the Cauchy data and then reformulated in terms of Maxwell solutions. The latter is employed to quantize the field in the framework of Dimock. Finally, the resulting algebra of observables is shown to satisfy the wave equation with the usual canonical commutation relations.Comment: 17 pages, 1 figure, typset in RevTeX4. This version contains substantial revisions in the discussion of the Cauchy problem for the generalized Maxwell field equatio

The gravitational redshift of boson stars

We investigate the possible gravitational redshift values for boson stars with a self-interaction, studying a wide range of possible masses. We find a limiting value of $z_{lim} \simeq 0.687$ for stable boson star configurations. We compare theoretical expectation with the observational capabilities in several different wavebands, concluding that direct observation of boson stars by this means will be extremely challenging. X-ray spectroscopy is perhaps the most interesting possibility.Comment: 7 pages RevTeX file with five figures incorporated (uses RevTeX and psfig

Time transfer and frequency shift to the order 1/c^4 in the field of an axisymmetric rotating body

Within the weak-field, post-Newtonian approximation of the metric theories of gravity, we determine the one-way time transfer up to the order 1/c^4, the unperturbed term being of order 1/c, and the frequency shift up to the order 1/c^4. We adapt the method of the world-function developed by Synge to the Nordtvedt-Will PPN formalism. We get an integral expression for the world-function up to the order 1/c^3 and we apply this result to the field of an isolated, axisymmetric rotating body. We give a new procedure enabling to calculate the influence of the mass and spin multipole moments of the body on the time transfer and the frequency shift up to the order 1/c^4. We obtain explicit formulas for the contributions of the mass, of the quadrupole moment and of the intrinsic angular momentum. In the case where the only PPN parameters different from zero are beta and gamma, we deduce from these results the complete expression of the frequency shift up to the order 1/c^4. We briefly discuss the influence of the quadrupole moment and of the rotation of the Earth on the frequency shifts in the ACES mission.Comment: 17 pages, no figure. Version 2. Abstract and Section II revised. To appear in Physical Review

Fourth order gravity: equations, history, and applications to cosmology

The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e., the details how within fourth order gravity with L= R + R^2 the inflationary phase of cosmic evolution turns out to be a transient attractor. Finally, the Bicknell theorem, i.e. the conformal relation from fourth order gravity to scalar-tensor theory, will be shortly presented.Comment: 51 pages, LaTeX, no figure, lecture for 42nd Karpacz Winter School 6.-11.2.06, references 99-109 and related comments are adde

Interior Weyl-type Solutions of the Einstein-Maxwell Field Equations

Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational potentials are studied. General results for these metrics are presented which extend previous work of Majumdar. In particular, it is shown that for any solution of the field equations exhibiting such a Weyl-type relationship, there exists a relationship between the matter density, the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter, a number of exact solutions are presented in closed form which generalise the Schwarzschild interior solution. Some of these solutions exhibit functional relations between the electric and gravitational potentials different to the quadratic one of Weyl. All the non-dust solutions are well-behaved and, by matching them to the Reissner-Nordstr\"{o}m solution, all of the constants of integration are identified in terms of the total mass, total charge and radius of the source. This is done in detail for a number of specific examples. These are also shown to satisfy the weak and strong energy conditions and many other regularity and energy conditions that may be required of any physically reasonable matter distribution.Comment: 21 pages, RevTex, to appear in General Relativity and Gravitatio

Spin-Raising Operators and Spin-3/2 Potentials in Quantum Cosmology

Local boundary conditions involving field strengths and the normal to the boundary, originally studied in anti-de Sitter space-time, have been recently considered in one-loop quantum cosmology. This paper derives the conditions under which spin-raising operators preserve these local boundary conditions on a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component spinor analysis of the four potentials of the totally symmetric and independent field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It is shown that such boundary conditions can only be imposed in a flat Euclidean background, for which the gauge freedom in the choice of the potentials remains.Comment: 13 pages, plain-tex, recently appearing in Classical and Quantum Gravity, volume 11, April 1994, pages 897-903. Apologies for the delay in circulating the file, due to technical problems now fixe

Gravity of a static massless scalar field and a limiting Schwarzschild-like geometry

We study a set of static solutions of the Einstein equations in presence of a massless scalar field and establish their connection to the Kantowski-Sachs cosmological solutions based on some kind of duality transformations. The physical properties of the limiting case of an empty hyperbolic spacetime (pseudo-Schwarzschild geometry) are analyzed in some detail.Comment: 13 pages, 4 figure