Thoralf Chrobok

Shear-free rotating inflation

We demonstrate the existence of shear-free cosmological models with rotation and expansion which support inflationary scenarios. The corresponding metrics belong to the family of spatially homogeneous models with the geometry of the closed universe (Bianchi type IX). We show that the global vorticity does not prevent inflation and can even accelerate it.

On closed rotating worlds

A new solution for the stationary closed world with rigid rotation is obtained for the spinning fluid source. It is found that the spin and the vorticity are locally balanced. This model qualitatively shows that the local rotation of cosmological matter can be indeed related to the global cosmic vorticity, provided the total angular momentum of the closed world is vanishing.

Rotation in string cosmology

We describe exact cosmological solutions with rotation and expansion in the low-energy effective string theory. These models are spatially homogeneous (closed Bianchi type IX) and they belong to the family of shear-free metrics which are causal (no closed timelike curves are allowed), admit no parallax effects and do not disturb the isotropy of the background radiation. The dilaton and the axion fields are nontrivial, in general, and we consider both cases with and without the central charge (effective cosmological constant).

On special- and general-relativistic thermodynamics

In reviewing approaches to the special- and general-relativistic theory of irreversible thermodynamical processes near equilibrium, problems of this procedure and possible solutions are discussed.

Shock wave polarizations and optical metrics in the Born and the Born–Infeld electrodynamics

We analyze the behavior of shock waves in nonlinear theories of electrodynamics. For this, by use of generalized Hadamard step functions of increasing order, the electromagnetic potential is developed in a series expansion near the shock wave front. This brings about a corresponding expansion of the respective electromagnetic field equations which allows for deriving relations that determine the jump coefficients in the expansion series of the potential. We compute the components of a suitable gauge-normalized version of the jump coefficients given for a prescribed tetrad compatible with the shock front foliation. The solution of the first-order jump relations shows that, in contrast to linear Maxwells electrodynamics, in general the propagation of shock waves in nonlinear theories is governed by optical metrics and polarization conditions describing the propagation of two differently polarized waves (leading to a possible appearance of birefringence). In detail, shock waves are analyzed in the Born and Born-Infeld theories verifying that the Born-Infeld model exhibits no birefringence and the Born model does. The obtained results are compared to those ones found in literature. New results for the polarization of the two different waves are derived for Born-type electrodynamics.

Thermodynamical equilibrium and space-time geometry - a survey

Based on the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a framework for special- and general-relativistic continuum thermodynamics. A general entropy 4-vector, containing particle, energy momentum, and spin density contributions, is introduced. In a second part, we confine this framework to General Relativity Theory and show exemplarily that the incorporation of gravitational field equations has strong consequences for relativistic continuum thermodynamics.

ON THE CONSTRUCTION OF SHEARFREE COSMOLOGICAL MODELS

Using the proper time description and the usual cosmological observer field, it is possible to construct general space–time metrics representing a class of shearfree cosmological models.

Classification of image distortions in terms of Petrov types

An observer surrounded by sufficiently small spherical lightsources at a fixed distance will see a pattern of elliptical images distributed over the sky, owing to the distortion effect (shearing effect) of the spacetime geometry upon light bundles. In lowest non-trivial order with respect to the distance, this pattern is completely determined by the conformal curvature tensor (Weyl tensor) at the observation event. In this paper we derive formulae that allow one to calculate these distortion patterns in terms of the Newman-Penrose formalism. Then we represent the distortion patterns graphically for all Petrov types, and we discuss their dependence on the velocity of the observer.

Screening and Absorption of Gravitation in Pre-Relativistic and Relativistic Theories

After commenting on the early search for a mechanism explaining the Newtonian action-at-a-distance gravitational law we review non-Newtonian effects occurring in certain ansatzes for shielding, screening and absorption effects in pre-relativistic theories of gravity. Mainly under the aspect of absorption and suppression (or amplification), we then consider some implications of these ansatzes for relativistic theories of gravity and discuss successes and problems in establishing a general framework for a comparison of alternative relativistic theories of gravity. We examine relativistic representatives of theories with absorption and suppression (or amplification) effects, such as fourth-order theories, tetrad theories and the Einstein-Cartan-Kibble-Sciama theory.

Non-Perfect-Fluid Space-Times in Thermodynamic Equilibrium and Generalized Friedmann Equations

We determine the energy-momentum tensor of nonperfect fluids in thermodynamic equilibrium and, respectively, near to it. To this end, we derive the constitutive equations for energy density and isotropic and anisotropic pressure as well as for heat-flux from the corresponding propagation equations and by drawing on Einstein’s equations. Following Obukhov on this, we assume the corresponding space-times to be conform-stationary and homogeneous. This procedure provides these quantities in closed form, that is, in terms of the structure constants of the three-dimensional isometry group of homogeneity and, respectively, in terms of the kinematical quantities expansion, rotation, and acceleration. In particular, we find a generalized form of the Friedmann equations. As special cases we recover Friedmann and Godel models as well as nontilted Bianchi solutions with anisotropic pressure. All of our results are derived without assuming any equations of state or other specific thermodynamic conditions a priori. For the considered models, results in literature are generalized to rotating fluids with dissipative fluxes.