Contributions to the relativistic mechanics of continuous media

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

Propagation of High-Frequency Electromagnetic Waves Through a Magnetized Plasma in Curved Spaces-Time. II. Application of the Asymptotic Approximation

This is the second of two papers on the propagation of high-frequency electromagnetic waves through an inhomogeneous, non-stationary plasma in curved space-time. By applying the general two-scale W.K.B. method developed in part I to the basic wave equation, derived also in that paper, we here obtain the dispersion relation, the rays, the polarization states and the transport laws for the amplitudes of these waves. In an unmagnetized plasma the transport preserves the helicity and the eccentricity of the polarization state along each ray; the axes of the polarization ellipse rotate along a ray, relative to quasiparallely displaced directions, at a rate determined by the vorticity of the electron fluid; and the norm of the amplitude changes according to a conservation law which can be interpreted as the constancy of the number of quasiphotons. In a magnetized plasma the polarization state changes differently for ordinary and extraordinary waves, according to the angle between the wavenormal and the background magnetic field, and under specified approximation conditions the direction of polarization of linearly polarized waves undergoes a generalized Faraday rotation

Joins for (Augmented) Simplicial Sets

We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $\Delta$.Comment: 8 page

The damping of gravitational waves in dust

We examine a simple model of interaction of gravitational waves with matter (primarily represented by dust). The aim is to investigate a possible damping effect on the intensity of gravitational wave when passing through media. This might be important for gravitational wave astronomy when the sources are obscured by dust or molecular clouds.Comment: 7 pages, accepted to Phys. Sc

Cosmology With A Dark Refraction Index

We review Gordon's optical metric and the transport equations for the amplitude and polarization of a geometrical optics wave traveling in a gravity field. We apply the theory to the FLRW cosmologies by associating a refraction index with the cosmic fluid. We then derive an expression for the accumulated effect of a refraction index on the distance redshift relations and fit the Hubble curve of current supernova observations with a non-accelerating cosmological model. We also show that some observational effects caused by inhomogeneities, e.g. the Sachs-Wolfe effect, can be interpreted as being caused by an effective index of refraction, and hence this theory could extend to other speed of light communications such as gravitational radiation and neutrino fluxes.Comment: 21 pages, 3 figure

Newtonian limits of warp drive spacetimes

We find a class of warp drive spacetimes possessing Newtonian limits, which we then determine. The same method is used to compute Newtonian limits of the Schwarzschild solution and spatially flat Friedmann-Robertson-Walker cosmological models.Comment: 9 pages; v2: major changes; v3: misprints correcte

Incorporation of Spacetime Symmetries in Einstein's Field Equations

In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form that fully incorporates the character of the symmetry. The method is being expressed in a covariant formalism using the framework of a double congruence. The basic notion on which it is based is that of the geometrisation of a general symmetry. As a special application of our general method we consider the case of a spacelike conformal Killing vector field on the spacetime manifold regarding special types of matter fields. New perspectives in General Relativity are discussed.Comment: 41 pages, LaTe

Five-dimensional vacuum Einstein spacetimes in C-metric like coordinates

A 5-dimensional Einstein spacetime with (non)vanishing cosmological constant is analyzed in detail. The metric is in close analogy with the 4-dimensional massless uncharged C-metric in many aspects. The coordinate system, horizons and causal structures, relations to standard de Sitter, anti de Sitter and Minkowski vacua are investigated. After a boost and Kaluza-Klein reduction, we get an exact solution of 4-dimensional Einstein-Maxwell-Liouville theory which reduces to a solution to Einstein-Liouville theory in the limit of zero boost velocity and to that of Einstein-Maxwell-diliton theory in the case of zero cosmological constant.Comment: 18 pages, 3 figures. Minor modifications, version appeared in Mod. Phys. Lett.