Gravitational Solitons and Monodromy Transform Approach to Solution of Integrable Reductions of Einstein Equations

In this paper the well known Belinskii and Zakharov soliton generating transformations of the solution space of vacuum Einstein equations with two-dimensional Abelian groups of isometries are considered in the context of the so called "monodromy transform approach", which provides some general base for the study of various integrable space - time symmetry reductions of Einstein equations. Similarly to the scattering data used in the known spectral transform, in this approach the monodromy data for solution of associated linear system characterize completely any solution of the reduced Einstein equations, and many physical and geometrical properties of the solutions can be expressed directly in terms of the analytical structure on the spectral plane of the corresponding monodromy data functions. The Belinskii and Zakharov vacuum soliton generating transformations can be expressed in explicit form (without specification of the background solution) as simple (linear-fractional) transformations of the corresponding monodromy data functions with coefficients, polynomial in spectral parameter. This allows to determine many physical parameters of the generating soliton solutions without (or before) calculation of all components of the solutions. The similar characterization for electrovacuum soliton generating transformations is also presented.Comment: 8 pages, 1 figure, LaTeX2e; based on a talk given at the International Conference 'Solitons, Collapses and Turbulence: Achievements, Developments and Perspectives', (Landau Institute for Theoretical Physics, Chernogolovka, Moscow region, Russia, August 3 -- 10, 1999); as submitted to Physica

Anisotropic Cosmological Models with Energy Density Dependent Bulk Viscosity

An analysis is presented of the Bianchi type I cosmological models with a bulk viscosity when the universe is filled with the stiff fluid $p = \epsilon$ while the viscosity is a power function of the energy density, such as $\eta = \alpha |\epsilon|^n$. Although the exact solutions are obtainable only when the $2n$ is an integer, the characteristics of evolution can be clarified for the models with arbitrary value of $n$. It is shown that, except for the $n = 0$ model that has solutions with infinite energy density at initial state, the anisotropic solutions that evolve to positive Hubble functions in the later stage will begin with Kasner-type curvature singularity and zero energy density at finite past for the $n> 1$ models, and with finite Hubble functions and finite negative energy density at infinite past for the $n < 1$ models. In the course of evolution, matters are created and the anisotropies of the universe are smoothed out. At the final stage, cosmologies are driven to infinite expansion state, de Sitter space-time, or Friedman universe asymptotically. However, the de Sitter space-time is the only attractor state for the $n <1/2$ models. The solutions that are free of cosmological singularity for any finite proper time are singled out. The extension to the higher-dimensional models is also discussed

Effects of the Shear Viscosity on the Character of Cosmological Evolution

Bianchi type I cosmological models are studied that contain a stiff fluid with a shear viscosity that is a power function of the energy density, such as $\zeta = \alpha \epsilon^n$. These models are analyzed by describing the cosmological evolutions as the trajectories in the phase plane of Hubble functions. The simple and exact equations that determine these flows are obtained when $n$ is an integer. In particular, it is proved that there is no Einstein initial singularity in the models of $0\leq n < 1$. Cosmologies are found to begin with zero energy density and in the course of evolution the gravitational field will create matter. At the final stage, cosmologies are driven to the isotropic Fnedmann universe. It is also pointed out that although the anisotropy will always be smoothed out asymptotically, there are solutions that simultaneously possess non-positive and non-negative Hubble functions for all time. This means that the cosmological dimensional reduction can work even if the matter fluid having shear viscosity. These characteristics can also be found in any-dimensional models

Hyperbolic Kac-Moody Algebras and Chaos in Kaluza-Klein Models

Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinsky, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike ("cosmological") singularity disappears in spacetime dimensions $D= d+1>10$. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic Kac-Moody algebra. In this letter, we show that the same connection applies to pure gravity in any spacetime dimension $\geq 4$, where the relevant algebras are $AE_d$. In this way the disappearance of chaos in pure gravity models in $D > 10$ dimensions becomes linked to the fact that the Kac-Moody algebras $AE_d$ are no longer hyperbolic for $d > 9$.Comment: 13 pages, 1 figur

New Axisymmetric Stationary Solutions of Five-dimensional Vacuum Einstein Equations with Asymptotic Flatness

New axisymmetric stationary solutions of the vacuum Einstein equations in five-dimensional asymptotically flat spacetimes are obtained by using solitonic solution-generating techniques. The new solutions are shown to be equivalent to the four-dimensional multi-solitonic solutions derived from particular class of four-dimensional Weyl solutions and to include different black rings from those obtained by Emparan and Reall.Comment: 6 pages, 3 figures;typos corrected, presentations improved, references added;accepted versio

Rotating Black Holes on Kaluza-Klein Bubbles

Using the solitonic solution generating techniques, we generate a new exact solution which describes a pair of rotating black holes on a Kaluza-Klein bubble as a vacuum solution in the five-dimensional Kaluza-Klein theory. We also investigate the properties of this solution. Two black holes with topology S^3 are rotating along the same direction and the bubble plays a role in holding two black holes. In static case, it coincides with the solution found by Elvang and Horowitz.Comment: 16 pages, 1 figure, minor correctio

Quantum field aspect of Unruh problem

It is shown using both conventional and algebraic approach to quantum field theory that it is impossible to perform quantization on Unruh modes in Minkowski spacetime. Such quantization implies setting boundary condition for the quantum field operator which changes topological properties and symmetry group of spacetime and leads to field theory in two disconnected left and right Rindler spacetimes. It means that "Unruh effect" does not exist.Comment: LaTeX, 13 pages, 1 figur

The Jeans Instability in Presence of Viscous Effects

An analysis of the gravitational instability in presence of dissipative effects is addressed. In particular, the standard Jeans Mechanism and the generalization in treating the Universe expansion are both analyzed when bulk viscosity affects the first-order Newtonian dynamics. As results, the perturbation evolution is founded to be damped by dissipative processes and the top-down mechanism of structure fragmentation is suppressed. In such a scheme, the value of the Jeans Mass remains unchanged also in presence of viscosity.Comment: 13 pages, 2 figure

Inhomogeneous M-Theory Cosmologies

We study a class of inhomogeneous and anisotropic $G_2$ string cosmological models. In the case of separable $G_2$ models we show that the governing equations reduce to a system of ordinary differential equations. We focus on a class of separable $G_2$ M-theory cosmological models, and study their qualitative behaviour (a class of models with time-reversed dynamics is also possible). We find that generically these inhomogeneous M-theory cosmologies evolve from a spatially inhomogeneous and negatively curved model with a non-trivial form field towards spatially flat and spatially homogeneous dilaton-moduli-vacuum solutions with trivial form--fields. The late time behaviour is the same as that of spatially homogeneous models previously studied. However, the inhomogeneities are not dynamically insignificant at early times in these models.Comment: 18 pages, 0 figures, REVTEX, AMSfonts; To appear in Jour. Math. Phy

On the Gravitational Collapse of a Gas Cloud in Presence of Bulk Viscosity

We analyze the effects induced by the bulk viscosity on the dynamics associated to the extreme gravitational collapse. Aim of the work is to investigate whether the presence of viscous corrections to the evolution of a collapsing gas cloud influence the fragmentation process. To this end we study the dynamics of a uniform and spherically symmetric cloud with corrections due to the negative pressure contribution associated to the bulk viscosity phenomenology. Within the framework of a Newtonian approach (whose range of validity is outlined), we extend to the viscous case either the Lagrangian, either the Eulerian motion of the system and we treat the asymptotic evolution in correspondence to a viscosity coefficient of the form $\zeta=\zeta_0 \rho^{nu}$ ($\rho$ being the cloud density and $\zeta_0=const.$). We show how, in the adiabatic-like behavior of the gas (i.e. when the politropic index takes values $4/3<\gamma\leq5/3$), density contrasts acquire, asymptotically, a vanishing behavior which prevents the formation of sub-structures. We can conclude that in the adiabatic-like collapse the top down mechanism of structures formation is suppressed as soon as enough strong viscous effects are taken into account. Such a feature is not present in the isothermal-like (i.e. $1\leq\gamma<4/3$) collapse because the sub-structures formation is yet present and outlines the same behavior as in the non-viscous case. We emphasize that in the adiabatic-like collapse the bulk viscosity is also responsible for the appearance of a threshold scale beyond which perturbations begin to increase.Comment: 13 pages, no figur