Heinz Dehnen

Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity

We analyze locally anisotropic configurations modeled by anholonomic frames with associated nonlinear connections in general relativity, affine–Poincarè and/or de Sitter gauge gravity and Kaluza–Klein theories. A suitable geometrical formalism for theories with higher order anisotropies and non compactified extra dimensions is introduced. We give a mostly self–containing review of some aspects of gauge models of gravity and discuss their anholonomic generalizations and the conditions of equivalence with the Einstein gravity in arbitrary dimensions. New classes of cosmological solutions describing Friedmann–Robertson–Walker like universes with resolution ellipsoid or torus symmetry.

NONLINEAR CONNECTIONS AND NEARLY AUTOPARALLEL MAPS IN GENERAL RELATIVITY

We apply the method of moving anholonomic frames with associated nonlinear connections to the (pseudo) Riemannian space geometry and examine the conditions when locally anisotropic structures (Finsler like and more general ones) could be modeled in the general relativity theory and/or Einstein–Cartan–Weyl extensions [1]. New classes of solutions of the Einstein equations with generic local anisotropy are constructed. We formulate the theory of nearly autoparallel (na) maps generalizing the conformal transforms and formulate the Einstein gravity theory on na–backgrounds provided with a set of na–map invariant conditions and local conservation laws. There are illustrated some examples when vacuum Einstein fields are generated by Finsler like metrics and chains of na–maps.

Scalar field pressure in induced gravity with Higgs potential and dark matter

A model of induced gravity with a Higgs potential is investigated in detail in view of the pressure components related to the scalar-field excitations. The physical consequences emerging as an artifact due to the presence of these pressure terms are analysed in terms of the constraints parting from energy density, solar-relativistic effects and galactic dynamics along with the dark matter halos.

Non-minimal pp-wave Einstein-Yang-Mills-Higgs model: color cross-effects induced by curvature

Non-minimal interactions in the pp-wave Einstein–Yang–Mills–Higgs (EYMH) model are shown to give rise to color cross-effects analogous to the magneto-electricity in the Maxwell theory. In order to illustrate the significance of these color cross-effects, we reconstruct the effective (associated, color, and color-acoustic) metrics for the pp-wave non-minimal seven-parameter EYMH model with parallel gauge and scalar background fields. Then these metrics are used as hints for obtaining explicit exact solutions of the non-minimally extended Yang–Mills and Higgs equations for the test fields propagating in the vacuum interacting with curvature. The influence of the non-minimal coupling on the test particle motion is interpreted in terms of the so-called trapped surfaces, introduced in the Analog Gravity theory.

Density perturbations in a cosmological de Donder gauge

Density perturbations are considered during the radiation-dominated and the dust-dominated periods of the expanding universe. The perturbations are taken to have spherical symmetry and the investigation is carried out in the de Donder gauge. In order to guarantee the energy-momentum conservation of the perturbation in the de Donder gauge a compatibility condition is obtained. Equations for the propagation of a spherically symmetric perturbation in linear approximation on a FRW cosmological background are presented. It turns out that the evolutiontendency of the formation is mainly predicted by the state of the cosmic background. A radiation-dominated universe does not stimulate growth processes; the perturbation will be in a frozen state or it will diffuse. It is found that the dust-dominated universe stimulates the perturbation mass to grow. The rate of this cosmic affected growing process is proportional toR−1 (R being the scale factor of the universe), so that it seems that almost all galaxies were formed at the beginning of the present dust-dominated era.

THERMALIZED NEWTONIAN BOSE STARS

We consider star models consisting of spin 0 particles interacting only gravitationally, e.g. Higgs-particles as possible dark matter objects. The particle gas of finite temperature is treated according to the Bose-Einstein-statistics in its non- relativistic limit; then the use of Newtonian gravity is sufficient too. The limits of these restrictions are estimated. The local temperature is determined with the use of energy conservation. The mass-radius relation of the objects and their further behaviours as Bose-Einstein-condensation in the outer regions are calculated. We find strong similarities with the features of white dwarfs and neutron stars.

Gravitating dyons in Vaidya geometry

Gravitating monopoles and dyons in Einstein–Yang–Mills (EYM) or Einstein–Yang–Mills–Higgs (EYMH) systems have been extensively studied for various curved space–times, including those of black holes. We construct dyonic solutions of the EYMH theory in Vaidya space–time using a set of generalized Julia–Zee ansatz for the fields. It is found that the dyonic charge is static in nature and it does not contribute to the energy of the null dust.

Spherically symmetric cosmological perturbations in the de Donder gauge (II)

In the framework of a previously developed procedure the evolution of small spherically symmetric perturbations in a homogeneous R-W-F universe is analyzed. It turns out that the evolution tendency is mainly predicted by the state of the cosmic background. In the radiation dominated period the universe does not stimulate growing processes, a perturbation will be in a frozen state or it will diffuse. It is found that a dust dominated universe stimulates the perturbation masses to grow. The rate of this cosmic affected growing process is proportional to (R)−1/2 (R being the scale factor). Consequently almost all galaxies were formed at the beginning of the dust dominated era.