A rotating cylinder in an asymptotically locally anti-de Sitter background

A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Godel solution. An exact solution for the exterior solution is found which depends both on the rotation of the interior and on its radius. For values of these parameters less than a certain limit, the exterior solution is shown to be locally isomorphic to the Linet-Tian solution. For values larger than another limit, it is shown that the exterior solution extends into a region which contains closed timelike curves. At large distances from the source, the space-time is shown to be asymptotic locally to anti-de Sitter space.Comment: To appear in Classical and Quantum Gravit

Transport Far From Equilibrium --- Uniform Shear Flow

The BGK model kinetic equation is applied to spatially inhomogeneous states near steady uniform shear flow. The shear rate of the reference steady state can be large so the states considered include those very far from equilibrium. The single particle distribution function is calculated exactly to first order in the deviations of the hydrodynamic field gradients from their values in the reference state. The corresponding non-linear hydrodynamic equaitons are obtained and the set of transport coefficients are identified as explicit functions of the shear rate. The spectrum of the linear hydrodynamic equation is studied in detail and qualitative differences from the spectrum for equilibrium fluctuations are discussed. Conditions for instabilities at long wavelengths are identified and disccused.Comment: 32 pages, 1 figure, RevTeX, submitted to Phys. Rev.

G\"{o}del-type universes in f(R) gravity

The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without a dark energy matter component. If gravity is governed by a $f(R)$ theory a number of issues should be reexamined in this framework, including the violation of causality problem on nonlocal scale. We examine the question as to whether the $f(R)$ gravity theories permit space-times in which the causality is violated. We show that the field equations of these $f(R)$ gravity theories do not exclude solutions with breakdown of causality for a physically well-motivated perfect-fluid matter content. We demonstrate that every perfect-fluid G\"{o}del-type solution of a generic $f(R)$ gravity satisfying the condition $df/dR > 0$ is necessarily isometric to the G\"odel geometry, and therefore presents violation of causality. This result extends a theorem on G\"{o}del-type models, which has been established in the context of general relativity. We also derive an expression for the critical radius $r_c$ (beyond which the causality is violated) for an arbitrary $f(R)$ theory, making apparent that the violation of causality depends on both the $f(R)$ gravity theory and the matter content. As an illustration, we concretely take a recent $f(R)$ gravity theory that is free from singularities of the Ricci scalar and is cosmologically viable, and show that this theory accommodates noncausal as well as causal G\"odel-type solutions.Comment: 7 pages, V3: Version to appear in Phys. Rev. D (2009), typos corrected, the generality of our main results is emphasized. The illustrative character of a particular theory is also made explici

Wigner-Moyal description of free variable mass Klein-Gordon fields

A system of coupled kinetic transport equations for the Wigner distributions of a free variable mass Klein-Gordon field is derived. This set of equations is formally equivalent to the full wave equation for electromagnetic waves in nonlinear dispersive media, thus allowing for the description of broadband radiation-matter interactions and the associated instabilities. The standard results for the classical wave action are recovered in the short wavelength limit of the generalized Wigner-Moyal formalism for the wave equation.Comment: 9 pages, accepted for publication in Journal of Mathematical Physic

Stability of Uniform Shear Flow

The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at any finite shear rate for sufficiently long wavelength perturbations. The analysis is extended to larger shear rates using a low density model kinetic equation. Direct Monte Carlo Simulation of this equation is computed with a hydrodynamic description including non Newtonian rheological effects. The hydrodynamic description of the instability is in good agreement with the direct Monte Carlo simulation for $t < 50t_0$, where $t_0$ is the mean free time. Longer time simulations up to $2000t_0$ are used to identify the asymptotic state as a spatially non-uniform quasi-stationary state. Finally, preliminary results from molecular dynamics simulation showing the instability are presented and discussed.Comment: 25 pages, 9 figures (Fig.8 is available on request) RevTeX, submitted to Phys. Rev.

Energy Conditions and Supernovae Observations

In general relativity, the energy conditions are invoked to restrict general energy-momentum tensors on physical grounds. We show that in the standard Friedmann-Lemaitre-Robertson-Walker approach to cosmological modelling where the equation of state of the cosmological fluid is unknown, the energy conditions provide model-independent bounds on the behavior of the distance modulus of cosmic sources as a function of the redshift. We use both the gold and the legacy samples of current type Ia supenovae to carry out a model-independent analysis of the energy conditions violation in the context of standard cosmology.Comment: 4 pages, 2 figures; v2: References added, misprints corrected, published in Phys.Rev.D in the present for