On a class of invariant coframe operators with application to gravity

Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives or quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The paper exhibits the class of operators that are invariant under a general change of coordinates, and, also, invariant under the global SO(1,3)-transformation of the coframe. A general class of field equations is constructed. We display two subclasses in it. The subclass of field equations that are derivable from action principles by free variations and the subclass of field equations for which spherical-symmetric solutions, Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the resulting metric is computed. Invoking the Geodesic Postulate, we find all the equations that are experimentally (by the 3 classical tests) indistinguishable from Einstein field equations. This family includes, of course, also Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the paper is an invariant formulation reminiscent of Cartan's structural equations. The article sheds light on the possibilities and limitations of the coframe gravity. It may also serve as a general procedure to derive covariant field equations

Matrix theory of gravitation

A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those theories (sec. 4.1). For the standard test cases (PPN scheme, Schwarzschild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.Comment: 24 page

BRST-antifield-treatment of metric-affine gravity

The metric-affine gauge theory of gravity provides a broad framework in which gauge theories of gravity can be formulated. In this article we fit metric-affine gravity into the covariant BRST--antifield formalism in order to obtain gauge fixed quantum actions. As an example the gauge fixing of a general two-dimensional model of metric-affine gravity is worked out explicitly. The result is shown to contain the gauge fixed action of the bosonic string in conformal gauge as a special case.Comment: 19 pages LATEX, to appear in Phys. Rev.

Projective Invariance and One-Loop Effective Action in Affine-Metric Gravity Interacting with Scalar Field

We investigate the influence of the projective invariance on the renormalization properties of the theory. One-loop counterterms are calculated in the most general case of interaction of gravity with scalar field.Comment: 10 pages, LATE

The Affine-Metric Quantum Gravity with Extra Local Symmetries

We discuss the role of additional local symmetries related to the transformations of connection fields in the affine-metric theory of gravity. The corresponding BRST transformations connected with all symmetries (general coordinate, local Lorentz and extra) are constructed. It is shown, that extra symmetries give the additional contribution to effective action which is proportional to the corresponding Nielsen-Kallosh ghost one. Some arguments are given, that there is no anomaly associated with extra local symmetries.Comment: 14 pages in LATEX (The version of paper accepted for publication in Class. Quant. Grav.

Core Overshoot: An Improved Treatment and Constraints from Seismic Data

We present a comprehensive set of stellar evolution models for Procyon A in an effort to guide future measurements of both traditional stellar parameters and seismic frequencies towards constraining the amount of core overshoot in Procyon A and possibly other stars. Current observational measurements of Procyon A when combined with traditional stellar modeling only place a large upper limit on overshoot of alphaOV < 1.1. By carrying out a detailed pulsation analysis, we further demonstrate, how p- and g-mode averaged spacings can be used to gain better estimates of the core size. For both p- and g-modes, the frequency spacings for models without overshoot are clearly separated from the models with overshoot. In addition, measurements of the l=0 averaged small p-mode spacings could be used to establish Procyon A's evolutionary stage. For a fixed implementation of overshoot and under favorable circumstances, the g-mode spacings can be used to determine the overshoot extent to an accuracy of +-0.05 Hp. However, we stress that considerable confusion is added due to the unknown treatment of the overshoot region. This ambiguity might be removed by analyzing many different stars. A simple non-local convection theory developed by Kuhfuss is implemented in our stellar evolution code and contrasted with the traditional approaches. We show that this theory supports a moderate increase of the amount of convective overshoot with stellar mass of Delta(alphaOV) = +0.10 between 1.5 Msun and 15 Msun. This theory places an upper limit on Procyon A's core overshoot extent of ~0.4 Hp which matches the limit imposed by Roxburgh's integral criterion.Comment: 45 pages, 26 figures, accepted in Ap

Pulsational instability of yellow hypergiants

Instability of population I (X=0.7, Y=0.02) massive stars against radial oscillations during the post-main sequence gravitational contraction of the helium core is investigated. Initial stellar masses are in the range from 65M_\odot to 90M_\odot. In hydrodynamic computations of self-exciting stellar oscillations we assumed that energy transfer in the envelope of the pulsating star is due to radiative heat conduction and convection. The convective heat transfer was treated in the framework of the theory of time-dependent turbulent convection. During evolutionary expansion of outer layers after hydrogen exhaustion in the stellar core the star is shown to be unstable against radial oscillations while its effective temperature is Teff > 6700K for Mzams=65M_\odot and Teff > 7200K for mzams=90M_\odot. Pulsational instability is due to the \kappa-mechanism in helium ionization zones and at lower effective temperature oscillations decay because of significantly increasing convection. The upper limit of the period of radial pulsations on this stage of evolution does not exceed 200 day. Radial oscillations of the hypergiant resume during evolutionary contraction of outer layers when the effective temperature is Teff > 7300K for Mzams=65M_\odot and Teff > 7600K for Mzams=90M_\odot. Initially radial oscillations are due to instability of the first overtone and transition to fundamental mode pulsations takes place at higher effective temperatures (Teff > 7700K for Mzams=65M_\odot and Teff > 8200K for Mzams=90M_\odot). The upper limit of the period of radial oscillations of evolving blueward yellow hypergiants does not exceed 130 day. Thus, yellow hypergiants are stable against radial stellar pulsations during the major part of their evolutionary stage.Comment: 20 pages, 7 gigures. Accepted for publication in Astronomy Letter

An assessment of Evans' unified field theory I

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe theta and a (metric compatible) Lorentz connection Gamma. These two potentials yield the field strengths torsion T and curvature R. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe theta to be proportional to four extended electromagnetic potentials A; these are assumed to encompass the conventional Maxwellian potential in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and typos removed, partly reformulated, taken care of M.W.Evans' rebutta

Presupernova Structure of Massive Stars

Issues concerning the structure and evolution of core collapse progenitor stars are discussed with an emphasis on interior evolution. We describe a program designed to investigate the transport and mixing processes associated with stellar turbulence, arguably the greatest source of uncertainty in progenitor structure, besides mass loss, at the time of core collapse. An effort to use precision observations of stellar parameters to constrain theoretical modeling is also described.Comment: Proceedings for invited talk at High Energy Density Laboratory Astrophysics conference, Caltech, March 2010. Special issue of Astrophysics and Space Science, submitted for peer review: 7 pages, 3 figure