From 2-Dimensional Surfaces to Cosmological Solutions

We construct perfect fluid metrics corresponding to spacelike surfaces invariant under a 1-dimensional group of isometries in 3-dimensional Minkowski space. Under additional assumptions we obtain new cosmological solutions of Bianchi type II, VI_0 and VII_0. The solutions depend on an arbitrary function of time, which can be specified in order to satisfy an equation of state.Comment: 12 pages, no figures, LaTeX2e, to be published in Class. Quant. Gra

Exponential-Potential Scalar Field Universes I: The Bianchi I Models

We obtain a general exact solution of the Einstein field equations for the anisotropic Bianchi type I universes filled with an exponential-potential scalar field and study their dynamics. It is shown, in agreement with previous studies, that for a wide range of initial conditions the late-time behaviour of the models is that of a power-law inflating FRW universe. This property, does not hold, in contrast, when some degree of inhomogeneity is introduced, as discussed in our following paper II.Comment: 16 pages, Plain LaTeX, 1 Figure to be sent on request, to appear in Phys. Rev.

Shear free solutions in General Relativity Theory

The Goldberg-Sachs theorem is an exact result on shear-free null geodesics in a vacuum spacetime. It is compared and contrasted with an exact result for pressure-free matter: shear-free flows cannot both expand and rotate. In both cases, the shear-free condition restricts the way distant matter can influence the local gravitational field. This leads to intriguing discontinuities in the relation of the General Relativity solutions to Newtonian solutions in the timelike case, and of the full theory to the linearised theory in the null case. It is a pleasure to dedicate this paper to Josh Goldberg.Comment: 17 pages, no figures. For GRG special issue in honor of Josh Goldber

Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas

We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein-Maxwell field equations for this gas becomes a dynamical system in a 4-dimensional phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3-dimensional sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H_{0} is negative. If H_{0} is positive, and depending on initial conditions, the trajectories end up in a curvature singularity that could be isotropic(singular "point") or anisotropic (singular "line"). In particular, for a sufficiently large initial value of the magnetic field it is always possible to obtain an anisotropic type of singularity in which the "line" points in the same direction of the field.Comment: 6 pages, 3 figures (accepted in General Relativity and Gravitation

Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Time-Symmetrization and Isotropization of Stiff-Fluid Kantowski-Sachs Universes

It is shown that growing-entropy stiff-fluid Kantowski-Sachs universes become time-symmetric (if they start with time-asymmetric phase) and isotropize. Isotropization happens without any inflationary era during the evolution since there is no cosmological term here. It seems that this approach is an alternative to inflation since the universe gets bigger and bigger approaching 'flatness'.Comment: 9 pages, no figure

Temperature and Polarization Patterns in Anisotropic Cosmologies

We study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII$_{0}$, VII$_{h}$ and IX) to illustrate the range of possible behaviour. We discuss the role of spatial curvature, shear and rotation in the geodesic equations for each model and establish some basic results concerning the symmetries of the patterns produced. We also give examples of the time-evolution of these patterns in terms of the Stokes parameters $I$, $Q$ and $U$.Comment: 24 pages, 7 Figures, submitted to JCAP. Revised version: numerous references added, text rewritten, and errors corrected

On the stability of the shear-free condition

The evolution equation for the shear is reobtained for a spherically symmetric anisotropic, viscous dissipative fluid distribution, which allows us to investigate conditions for the stability of the shear-free condition. The specific case of geodesic fluids is considered in detail, showing that the shear-free condition, in this particular case, may be unstable, the departure from the shear-free condition being controlled by the expansion scalar and a single scalar function defined in terms of the anisotropy of the pressure, the shear viscosity and the Weyl tensor or, alternatively, in terms of the anisotropy of the pressure, the dissipative variables and the energy density inhomogeneity.Comment: 19 pages Latex. To appear in Gen. Rel. Gra

Comparative Study of full QCD Hadron Spectrum and Static Quark Potential with Improved Actions

We investigate effects of action improvement on the light hadron spectrum and the static quark potential in two-flavor QCD for $a^{-1} \approx 1$ GeV and $m_{PS}/m_V = 0.7-0.9$. We compare a renormalization group improved action with the plaquette action for gluons, and the SW-clover action with the Wilson action for quarks. We find a significant improvement in the hadron spectrum by improving the quark action, while the gluon improvement is crucial for a rotationally invariant static potential. We also explore the region of light quark masses corresponding to $m_{PS}/m_V \geq 0.4$ on a 2.7 fm lattice using the improved gauge and quark action. A flattening of the potential is not observed up to 2 fm.Comment: LaTeX, 35 pages, 22 eps figures, uses revtex and eps

Equation of state for Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This methods is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise the equation of state in the form $p=-\Lambda+w_{1}\rho(a)+w_{2}a^{\beta}+0$ and energy density $\rho=\Lambda+\rho_{01}a^{-3(1+w)}+\rho_{02}a^{\beta}+\rho_{03}a^{-3}$, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data. We showed that the model with scaling fluid fits well to supernovae data. We found that $\Omega_{\text{m},0} \simeq 0.4$ and $n \simeq -1$ ($\beta = -3n$), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that $\Omega_{\text{m},0}=0.3$ then the favoured model is close to concordance $\Lambda$CDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in $\Lambda$CDM model, while intermediate distant SNIa should be fainter than in $\Lambda$CDM model. We also investigate whether the model with scaling fluid is actually preferred by data over $\Lambda$CDM model. As a result we find from the Akaike model selection criterion prefers the model with noninteracting scaling fluid.Comment: accepted for publication versio