Cover picture: When a source, e. g., a QSO, lies behind a foreground galaxy, its light bundle is affected by the individual stars of this galaxy. This microlensingeffect, so far observed in at least one QSO (see Sect. 12.4), leads to a change in the flux we observe from the source, relative to an unlensed source. The flux magnification depends sensitively on the position of the source relative to the stars in the galaxy. Here we see the magnification as a function of the relative source position; red and yellow indicates high magnification, green and blue low magnification. The superimposed white curves are the caustics produced by the stars, projected into the source plane. The figure (which is taken from Wambsganss, Witt, and Schneider. Astr. Astophys., 258. 591 (1992)) has been produced by combining the ray-shooting method (Sects. 10.6. and 11.2.5) with the parametric representation of caustics (Sect. 8.3.4). The parameters for the star field are 1(.=0.5. y =1(,= O. with all stars having the same mass. The shape of the acoustics is analyzed in Chap. 6.

Cover picture: When a source, e.g., a QSO, lies behind a foreground galaxy, its light boundle is affected by the individual stars ofthis galaxy. This microlensing effect, so far observed in at least one QSO (see Sect. 12.4), leads to a change in the flux we observe from the source, relative to an lInlensed source. The flux magnification depends sensitively on the position of the source relative to the stars in the galaxy. Here we see the magnification as a function of the relative source position: red and yellow indicates high magnification, green and blue low magnification. The superimposed white curves are the caustics produced by the stars, projected into the source plane. The figure (taken from Wambsganss, Witt, and Schneider, Asfr. Astrophys., 258, 591 (1992)) has been produced by combining the ray-shooting method (Sects. 10.6 and 11.2.5) with the parametric representation of caustics (Sect. 8.3.4). The parameters for the star field are K. = 0.5, ' Y = Kc= 0, with all stars having the same mass. The shape of the acoustics is analyzed in Chap. 6.

This is a translation from German of an article originally published inProceedings of the Mathematical-Natural Science Section of the Mainz Academy of Science and Literature, Nr. 11, 1961 (pp. 792–837) (printed by Franz Steiner and Co, Wiesbaden), which is Paper IV in the series ldquoExact Solutions of the Field Equations of General Relativity Theoryrdquo by Pascual Jordan, Jürgen Ehlers, Wolfgang Kundt and Rainer K. Sachs. The translation has been carried out by G. F. R. Ellis (Department of Applied Mathematics, University of Cape Town), assisted by P. K. S. Dunsby, so that this outstanding review paper can be readily accessible to workers in the field today. As far as possible, the translation has preserved both the spirit and the form of the original paper. Despite its age, it remains one of the best reviews available in this area

No abstract

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Dixon's approach to describe the dynamics of extended bodies in metric theories of gravity is elaborated. The exact, general relation between the center-of-mass 4-velocity and the 4-momentum is derived. Quasirigid bodies are defined, and their equations of motion are shown to be determinate for a given metric. Multipole approximations are considered, and the physical meaning of quasirigidity is investigated by establishing an approximate connection with continuum mechanics. G. Dixon has laid the foundations of an exact dynamics of extended bodies in metric theories of gravity. The purposes of this paper are (1) to extend Dixon's general theory by elaborating the center-of-mass description of arbitrary bodies, (2) to restrict the center-of-mass description to what we shall call quasirigid bodies, (3) to consider some properties of multipole approximations to the general theory, and (4) to establish a connection between continuum mechanics and the theory of quasirigid bodies.After a review of those definitions and results of Dixon's theory on which this work is based we derive in Section 2 a formula for the relativistic center-of-197

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The gravitational field generated by a gas whose one-particle distribution function obeys the Liouville equation is examined under the following assumptions: First, the distribution is locally isotropic in momentum space with respect to some world-velocity field; second, if the particles have rest-mass zero, the gas is irrotational. It is shown that the model is then either stationary or a Robertson-Walker model. The time dependence of the radius in the Robertson-Walker models is given in terms of integrals containing the distribution function.