Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes

The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org

Spherically symmetric steady states of galactic dynamics in scalar gravity

The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical way those problems, like the influence of the gravitational radiation on the dynamics, which are still beyond our present understanding of the physical model represented by the Einstein--Vlasov system. The present paper is devoted to derive the equations of the model and to prove the existence of spherically symmetric equilibria with finite radius.Comment: 13 pages, mistypos correcte

Critical collapse of collisionless matter - a numerical investigation

In recent years the threshold of black hole formation in spherically symmetric gravitational collapse has been studied for a variety of matter models. In this paper the corresponding issue is investigated for a matter model significantly different from those considered so far in this context. We study the transition from dispersion to black hole formation in the collapse of collisionless matter when the initial data is scaled. This is done by means of a numerical code similar to those commonly used in plasma physics. The result is that for the initial data for which the solutions were computed, most of the matter falls into the black hole whenever a black hole is formed. This results in a discontinuity in the mass of the black hole at the onset of black hole formation.Comment: 22 pages, LaTeX, 7 figures (ps-files, automatically included using psfig

The formation of black holes in spherically symmetric gravitational collapse

We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of radially outgoing null geodesics where the area radius r along each geodesic is bounded by 2M, the timelike lines $r=c\in [0,2M]$ are incomplete, and for r>2M the metric converges asymptotically to the Schwarzschild metric with mass M. The initial data that we construct guarantee the formation of a black hole in the evolution. We also give examples of such initial data with the additional property that the solutions exist for all $r\geq 0$ and all Schwarzschild time, i.e., we obtain global existence in Schwarzschild coordinates in situations where the initial data are not small. Some of our results are also established for the Einstein equations coupled to a general matter model characterized by conditions on the matter quantities.Comment: 36 pages. A corollary on global existence in Schwarzschild coordinates for data which are not small is added together with minor modification

Flat galaxies with dark matter halos - existence and stability

We consider a model for a flat, disk-like galaxy surrounded by a halo of dark matter, namely a Vlasov-Poisson type system with two particle species, the stars which are restricted to the galactic plane and the dark matter particles. These constituents interact only through the gravitational potential which stars and dark matter create collectively. Using a variational approach we prove the existence of steady state solutions and their nonlinear stability under suitably restricted perturbations.Comment: 39 page

Interplay of bulk and surface properties for steady-state measurements of minority carrier lifetimes

The measurement of the minority carrier lifetime is a powerful tool in the field of semiconductor material characterization as it is very sensitive to electrically active defects. Furthermore, it is applicable to a wide range of samples such as ingots or wafers. In this work, a systematic theoretical analysis of the steady-state approach is presented. It is shown how the measured lifetime relates to the intrinsic bulk lifetime for a given material quality, sample thickness, and surface passivation. This makes the bulk properties experimentally accessible by separating them from the surface effects. In particular, closed analytical solutions of the most important cases, such as passivated and unpassivated wafers and blocks are given. Based on these results, a criterion for a critical sample thickness is given beyond which a lifetime measurement allows deducing the bulk properties for a given surface recombination. These results are of particular interest for semiconductor material diagnostics especially for photovoltaic applications but not limited to this field.Comment: 17 pages, 3 figure

Hepatic Cytochrome P-450. A Proton Magnetic Relaxation Study of Microsomal, Solubilized and Partially Reconstituted Enzyme System

The longitudiJ:ial proton magnetic relaxation times, Ti, were measured from -5 to 40 °c for microsomal, solubilized and reconstituted cytochrome P-450 obtained from phenobarbital-induced rat livers. The paramagnetic contribution to the rates was derived by subtraction of the rates measured on dithionite-CO-reduced samples. The same values were obtained for microsomal P-450 on reduction with NADPH. PMR titratio.n by KCN yielded a dissociation constant of about 30 mM. This is three orders of magnitude larger than for metmyoglobin. It is concluded that the measured PMR rates are most likely due to the P-450 (and P-420) haem-iron while the 300/o non-haem iron found in both the microsomal and s olubilized P-450 is .ineffective for the PMR rates. These rates increase several times on isotopic dilution (D20 for H20) with the microsomes and diminish for the solubilized samples. Microsomes show 170/o residual, encaged, H20. Most of their paramagnetic PMR rate is due to the parama.gnetic iron located on the outside of microsomes. This is demonstrated by measurements with deuterated samples to which 190/o H20 had been added. Hence, the solubilized P-450 is homogeneous regarding PMR, but the microsomes are not