New Sedov-Type Solution of Isotropic Turbulence

The starting point lies in the results obtained by Sedov （1944） for isotropic turbulence with a self-preserving hypothesis. A careful consideration of the mathematical structure of the Karman-Howarth equation leads to an exact analysis of all cases possible and to all admissible solutions of the problem. I study this interesting problem from a new point of view. New solutions are obtained. Based on these exact solutions, some physical significant consequences of recent advances in the theory of self-preserved homogeneous statistical solution of the Navier-Stokes equations are presented.     

Long-Wavelength Approximation for String Cosmology with Barotropic Perfect Fluid

The field equations derived from the low energy string effective action with a matter tensor describing a perfect fluid with a barotropic equation of state are solved iteratively using the long-wavelength approximation, i.e. the field equations are expanded by the number of spatial gradients. In the zero order, a quasi-isotropic solution is presented and compared with the general solution of the pure dilaton gravity. Possible cosmological models are analyzed from the point of view of the pre-big bang scenario. The second order solutions are found and their growing and decaying parts are studied.     

Higher-dimensional vacuum solutions of Einstein's field equations

Some general solutions of the (general)D-dimensional vacuum Einstein field equations are obtained. The four-dimensional properties of matter are studied by investigating whether the higher-dimensional vacuum field equations reduce (formally) to Einstein's four-dimensional theory with matter. It is found that the solutions obtained give rise to an induced four-dimensional cosmological perfect fluid with a (physically reasonable) linear equation of state.     

Spherically Symmetric Solutions of Einstein's Vacuum Equations in Five Dimensions

Multi-dimensional spherically symmetric spacetimes are of interest in the study of higher-dimensional black holes (and solitons) and higher-dimensional cosmological models. In this paper we shall present a comprehensive investigation of solutions of the five-dimensional spherically symmetric vacuum Einstein field equations subject only to the condition of separability in the radial coordinate (but not necessarily in the remaining two coordinates). A variety of new solutions are found which generalize a number of previous results. The properties of these solutions are discussed with particular attention being paid to their possible astrophysical and cosmological applications. In addition, the four-dimensional properties of matter can be regarded as geometrical in origin by a reduction of the five-dimensional vacuum field equations to Einstein's four-dimensional theory with a non-zero energy-momentum tensor constituting the material source; we shall also be interested in the induced matter associated with the new five-dimensional solutions obtained.     

Cosmology as a search for overall equilibrium

The steps followed by Einstein when he first wrote on cosmology from the point of view of the general theory of relativity are revised. It is argued that his insightful line of thought leading to the introduction of the cosmological constant in the equations of motion has only one weakness: the constancy of the cosmological term, or what is the same, its independence of the matter content of the universe. Eliminating this feature, a simple and reasonable modification of the cosmological equations of motion is proposed. The solutions of the new cosmological equations give rise to a cosmological model that tries to approach the Einstein static solution. This model exhibits very appealing features in terms of fitting current observations. The text was submitted by the author in English.     

Domain Walls Strange Quark Matter in Einstein-Rosen Space-Time with Cosmological Constant and Heat Flow

In this paper, we have studied the solutions of Einstein field equations for domain walls with cosmological constant and heat flow in Einstein-Rosen cylindrical symmetric space-time when strange quark matter and normal matter attached to the domain walls. Some physical and kinematical features of the obtained cosmological model are studied and discussed.     

Single point velocity distributions in homogeneous isotropic turbulence

The starting point for this paper lies in the results obtained by Tatsumi (2004) for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the one-point velocity distribution function equation obtained by Tatsumi (2004) leads to an exact analysis of all possible cases and to all admissible solutions of the problem. This paper revisits this interesting problem from a new point of view, and obtains a new complete set of solutions. Based on these exact solutions, some physically significant consequences of recent advances in the theory of homogenous statistical solution of the Navier--Stokes equations are presented. The comparison with former theory was also made. The origin of non--Gaussian character could be deduced from the above exact solutions.     

Cosmological evolution in compactified Horava-Witten theory induced by matter on the branes

The combined Einstein equations and scalar equation of motion in the Horava-Witten scenario of the strongly coupled heterotic string compactified on a Calabi-Yau manifold are solved in the presence of additional matter densities on the branes. We take into account the universal Calabi-Yau modulus with potentials in the 5-d bulk and on the 3-branes, and allow for an arbitrary coupling of the additional matter to and an arbitrary equation of state. No ad hoc stabilization of the five dimensional radius is assumed. The matter densities are assumed to be small compared to the potential for on the branes; in this approximation we find solutions in the bulk which are exact in y and t. Depending on the coupling of the matter to and its equation of state, various solutions for the metric on the branes and in the 5-d bulk are obtained: solutions corresponding to a ”rolling radius”, and solutions with a static 5-d radius, which reproduce the standard cosmological evolution. Received: 8 April 2002 / Published online: 26 July 2002     

4D Homogeneous Isotropic Cosmological Models Generated by the 5D Vacuum

4-Dimensional homogeneous isotropic cosmological models obtained from solutions of vacuum 5-dimensional Einstein equations are considered. It is assumed, that the G₅₅-component of the 5D metric simulates matter in the comoving frame of reference. The observable 4D metric is defined up to conformal transformations of the metric of the 4D section g, with a conformal factor as a function of the component G₅₅. It is demonstrated, that the form of this function determines the matter equation of state. Possible equations of state are analyzed separately for flat, open and closed models.     

On hamiltonian formulation of cosmologies

Novello et al [1,2] have shown that it is possible to find a pair of canonically conjugate variables (written in terms of gauge-invariant variables) so as to obtain a Hamiltonian that describes the dynamics of a cosmological system. This opens up the way to the usual technique of quantization. Elbaz et al [4] have applied this method to the Hamiltonian formulation of FRW cosmological equations. This note presents a generalization of this approach to a variety of cosmologies. A general Schrödinger wave equation has been derived and exact solutions have been worked out for the stiff matter era for some cosmological models. It is argued that these solutions appear to hint at their possible relevance in the early phase of cosmological evolution.     

Thermodynamic parameterization

A new method of succesive construction of a solution is developed for problems of strongly nonequilibrium Boltzmann kinetics beyond normal solutions. Firstly, the method provides dynamic equations for any manifold of distributions where one looks for an approximate solution. Secondly, it gives a successive procedure of obtaining corrections to these approximations. The method requires meither small parameters, nor strong restrictions upon the initial approximation; it involves solutions of linear problems. It is concordant with the H-theorem at every step. In particular, for the Tamm-Mott-Smith approximation, dynamic equations are obtained, an expansion for the strong shock is introduced, and a linear equation for the first correction is found.     

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.     

The dynamical evolution of 3-space in a higher dimensional steady state universe

We investigate a class of cosmological solutions of Einstein’s field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject to two constraints that (i) the total volume scale factor of the universe is constant and (ii) the effective energy density is constant. We obtain various interesting new dynamics for the external space that yield a time varying deceleration parameter including oscillating cases when the flat/curved external and curved/flat internal spaces are considered. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the extra dimensions.     

Can electro-magnetic field,anisotropic source and varying Λ be sufficient to produce wormhole spacetime?

It is well known that solutions of general relativity which allow for traversable wormholes require the existence of exotic matter (matter that violates weak or null energy conditions (WEC or NEC)). In this article, we provide a class of exact solution for Einstein-Maxwell field equations describing wormholes assuming the erstwhile cosmological term Λ to be space variable, viz., Λ=Λ(r). The source considered here not only a matter entirely but a sum of matters i.e. anisotropic matter distribution, electromagnetic field and cosmological constant whose effective parts obey all energy conditions out side the wormhole throat. Here violation of energy conditions can be compensated by varying cosmological constant. The important feature of this article is that one can get wormhole structure, at least theoretically, comprising with physically acceptable matters.     

Diffraction equations for weak scattering reflective surface

In order to investigate the surface roughness dependence of speckle patterns, the complex-amplitude distribution of the speckle field should be obtained first. In previous studies, most investigators have treated this problem using the Fresnel or Fraunhofer diffraction equation. But for a weakly scattering reflective surface, when the observation plane is not parallel to the object plane, the Fresnel and Fraunhofer diffraction equations become inapplicable. Therefore, a reflective surface diffraction model (RSDM) is formed. When the difference between the RSDM and the transmission aperture diffraction model (TADM) is considered, then a general diffraction equation is presented. Considering the variations of the near-field approximation caused by coordinate system rotation, the near-field diffraction equation is derived. By introducing the far-field approximation, the far-field diffraction equation is obtained. The physical meanings of factors in the new equations are interpreted. Comparisons between the Fresnel and Fraunhofer diffraction equations and the newly derived ones show that the former are just the special cases of the latter. Finally, an application of these new diffraction equations is proposed.     

Scalar-tensor cosmologies with a potential in the general relativity limit: Time evolution

We consider Friedmann–Lemaître–Robertson–Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity. As an illustration we present an example of oscillating dark energy.     

Correlation effects,image charge effects and finite size in the macro-ion-electrolyte system: A field-theoretic approach

We consider a model of a macro-ion surrounded by small ions of an electrolyte solution. The finite size of ionic charge distributions of ions, and image charge effects are considered. From such a model it is possible to construct a statistical field theory with a single fluctuating field and derive physical interpretations for both the mean field and two-point correlation function. For point-like charges, at the level of a Gaussian (or saddle point) approximation, we recover the standard Poisson-Boltzmann equation. However, to include ionic correlation effects, as well as image charge effects of individual ions, we must go beyond this. From the field theory considered, it is possible to construct self-consistent approximations. We consider the simplest of these, namely the Hartree approximation. The Hartree equations take the form of two coupled equations. One is a modified Poisson-Boltzmann equation; the other describes both image charge effects on the individual ions, as well as correlations. Such equations are difficult to solve numerically, so we develop an (a WKB-like) approximation for obtaining approximate solutions. This, we apply to a uniformly charged rod in univalent electrolyte solution, for point like ions, as well as for extended spherically symmetric distributions of ionic charge on electrolyte ions. The solutions show how correlation effects and image charge effects modify the Poisson-Boltzmann result. Finite-size charge distributions of the ions reduce both the effects of correlations and image charge effects. For point charges, we test the WKB approximation by calculating a leading-order correction from the exact Hartree result, showing that the WKB-like approximation works reasonably well in describing the full solution to the Hartree equations. From these solutions, we also calculate an effective charge compensation parameter in an analytical formula for the interaction of two charged cylinders. Electronic supplementary material  Supplementary material in the form of a doc file available from the journal web page at and are accessible for authorised users.     

Isotropic and anisotropic dark energy models

In this review we discuss the evolution of the universe filled with dark energy with or without perfect fluid. In doing so we consider a number of cosmological models, namely Bianchi type I, III, V, VI₀, VI and FRW ones. For the anisotropic cosmological models we have used proportionality condition as an additional constrain. The exact solutions to the field equations in quadrature are found in case of a BVI model. It was found that the proportionality condition used here imposed severe restriction on the energy-momentum tensor, namely it leads to isotropic distribution of matter. Anisotropic BVI₀, BV, BIII and BIDE models with variable EoS parameter ω have been investigated by using a law of variation for the Hubble parameter. In this case the matter distribution remains anisotropic, though depending on the concrete model there appear different restrictions on the components of energy-momentum tensor. That is why we need an extra assumption such as variational a law for the Hubble parameter. It is observed that, at the early stage, the EoS parameter v is positive i.e. the universe was matter dominated at the early stage but at later time, the universe is evolving with negative values, i.e., the present epoch. DE model presents the dynamics of EoS parameter ω whose range is in good agreement with the acceptable range by the recent observations. A spatially homogeneous and anisotropic locally rotationally symmetric Bianchi-I space time filled with perfect fluid and anisotropic DE possessing dynamical energy density is studied. In the derived model, the EoS parameter of DE (ω^(de)) is obtained as time varying and it is evolving with negative sign which may be attributed to the current accelerated expansion of Universe. The distance modulus curve of derived model is in good agreement with SNLS type Ia supernovae for high redshift value which in turn implies that the derived model is physically realistic. A system of two fluids within the scope of a spatially flat and isotropic FRW model is studied. The role of the two fluids, either minimally or directly coupled in the evolution of the dark energy parameter, has been investigated. In doing so we have used three different ansatzs regarding the scale factor that gives rise to a variable decelerating parameter. It is observed that, in the non-interacting case, both the open and flat universes can cross the phantom region whereas in the interacting case only the open universe can cross the phantom region. The stability and acceptability of the obtained solution are also investigated.     

The cosmological constant is probably zero

It is suggested that the apparent cosmological constant is not necessarily zero but that zero is by far the most probable value. One requires some mechanism like a three-index antisymmetric tensor field or topological fluctuations of the metric which can give rise to an effective cosmological constant of arbitrary magnitude. The action of solutions of the euclidean field equations is most negative, and the probability is therefore highest, when this effective cosmological constant is very small.     

Back-reaction equations for isotropic cosmologies when nonconformal particles are created

A model proposed some years ago by Hartle to study the back reaction in a cosmological model due to the creation of massless non-conformally coupled particles is reexamined. The model consists of a spatially flat FRW spacetime with a classical source made of two perfect fluids one a radiative fluid and the other a baryonic fluid with the equation of state of dust, and it is assumed that the ratio of baryons to photons is small. The back-reaction equations for the cosmological scale factor are derived using a CTP (closed time path) effective action method. Making use of the connection, in the semiclassical context, between the CTP effective action and the influence functional in quantum statistical mechanics, improved back-reaction equations are derived which take into account the fluctuations of the stress-energy tensor of the quantum field. These new dynamical equations are real and causal and predict stochastic fluctuations for the cosmological scale factor.