Suchergebnisse

Spatially homogeneous cosmological models of Bianchi types I, V and IX (as well as their isotropic counterparts : the Einstein-de Sitter, open and closed Friedmann-Robertson-Walker (FRW) models, respectively), filled with a perfect fluid with an equation of state of the type p = (γ - 1 )ρ (γ = constant comprised between 1 and 2) are quantized in the framework of an ADM-type canonical quantization scheme introduced by Demaret and Moncrief.
This method which generalizes a method due to Lund and originally restricted to space-times filled with a pressureless fluid (p = 0) is based on Schutz's Hamiltonian theory of a relativistic perfect fluid, extending to general relativity Seliger and Whitham's velocity-potential version of classical hydrodynamics. It leads to a Schrödinger-like equation for the wave function of the universe, which admits a true physical interpretation in terms of probability as in orthodox quantum mechanics.
Contrary to Misner's early results based on a different quantization scheme, our method leads to the conclusion that, apart from a set of measure zero of models comprising FRW models as well as Bianchi models filled with a fluid with a stiff equation of state (p = ρ), all Bianchi models are non-singular, in the sense that the quantum wave function becomes zero at the classical singularity. Such a non-singular model can be interpreted as a contracting universe bouncing into an expanding universe, due to quantum gravitational fluctuations. A similar conclusion of non-singularity of a quantum Bianchi I universe has recently been obtained by Narlikar by using a different method of quantization, i.e. the method of path integration.

We give here a derivation of the general relativistic non adiabatic radial pulsation equation for spherically symmetric non rotating stars.
The influence of general relativistic corrections on the non adiabatic terms is treated up to the first order in the relativistic parameter. This implies that the unperturbed model must be considered in a state of "quasi-equilibrium" in the sense that its physical characteristics are slowly varying functions of time, due to the conversion of proper mass into energy, caused by the thermonuclear reactions.
Eckart's formalism is used to take into account the presence of a radiative or convective flux but the influence of the radiative viscosity terms is neglected in the derivation of the structure and pulsation equations.
Relativistic expressions are given for the vibrational stability coefficient and the secular root, the last one being used to recover and clarify the general relativistic secular instability of supermassive stars above a certain critical mass, found by Appenzeller and Kippenhahn.

Nous avons contruit la solution des équations générales décrivant les oscillations d'étoiles présentant un défaut de balance énergétique (thermal imbalance) en termes d'un développement asymptotique jusqu'au premier ordre en le paramètre Π/ts, où Π est la période d'oscillation adiabatique du mode fondamental et ts, une échelle de temps «lente» de l'ordre du temps de Kelvin-Helmholtz.
La solution ainsi obtenue nous permet de définir, sans ambiguïté, un coefficient de stabilité vibrationnelle pour un modèle stellaire arbitraire et de dériver une formule générale reliant les résultats d'analyses de stabilité en termes de δr et de δr/r.
L'application au cas simple de la contraction homologue nous permet de retrouver, d'une manière beaucoup plus directe, des résultats obtenus par Cox, Hansen et Davey (1973).

We calculate the linear e-folding time of pulsation for vibrationally unstable main-sequence supermassive stars (105-3.109M, where M0 is the solar mass), dynamically stabilized by a uniform or differential rotation, using some simplifying assumptions, none of which seems critical.
For the most massive stars, stabilized by a differential rotation (108-3.109 M0) which, following Hoyle and Fowler, could represent quasi-stellar objects, the e-folding time of pulsation is of the order of their life time (about 2.106 years) in the main-sequence stage, for a large interval of values of the central angular velocity of rotation. So, the phenomenon of vibrational instability cannot affect significantly the hydrogen burning stage of these stars.
Vibrational instability can, however, excite the adiabatic pulsations of some supermassive stars and so explain the optical periodicities observed for certain «quasars », like 3 C 345 and 3 C 273. If it is sufficiently violent, it can give birth to a stellar wind, which can be the source of the clouds of gas moving outward at very high velocities, which seem to be necessary to explain the multiple absorption red-shifts of some «quasars ».
Finally, supermassive stars dynamically stabilized by a differential rotation, but vibrationally unstable, could play an important rôle in the formation of the helium observed throughout the universe.