For a spatially flat Friedmann model with line element ds 2 = a 2 [da 2 /B(a) − dx 2 − dy 2 − dz 2 ], the 00-component of the Einstein field equation reads 8πGT 00 = 3/a 2 containing no derivative. For a nonlinear Lagrangian L(R), we obtain a second– order differential equation for B instead of the expected fourth-order equation. We discuss this equation for the curvature-saturated model propos...

A new numerical scheme for computing self-localized states--or solitons--of nonlinear waveguides is proposed. The idea behind the method is to transform the underlying equation governing the soliton, such as a nonlinear Schrödinger-type equation, into Fourier space and determine a nonlinear nonlocal integral equation coupled to an algebraic equation. The coupling prevents the numerical scheme f...

We investigate low temperature (T ) properties of three classical quantum statistics models: (I) the Fermi-Dirac equation, (II) the Boltzman equation, and (III) the Bose-Einstein equation. It is widely assumed that each of these equations is valid for all T > 0. For each equation we prove that this assumption leads to erroneous predictions as T → 0. Our approach to correct these errors gives ne...

For a spatially flat Friedmann model with line element ds 2 = a 2 [da 2 /B(a) − dx 2 − dy 2 − dz 2 ], the 00-component of the Einstein field equation reads 8πGT 00 = 3/a 2 containing no derivative. For a nonlinear Lagrangian L(R), we obtain a second– order differential equation for B instead of the expected fourth-order equation. We discuss this equation for the curvature-saturated model propos...

In this paper we consider a Z2 symmetrical 3-brane embedded in a 5-dimensional spacetime. We study the effective Einstein equation and acceleration condition in presence of the quintom dark energy fluid as the bulk matter field. It is shown that the time-dependent bulk quintom field induces a time-dependent cosmological constant on the brane. In the framework of the DGP model, the effective Ein...

We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite extension of spherically symmetric equilibria, which covers all these models simultaneously. In the Vlasov case the equilibria are characterized by a local ...

We study a Fokker-Planck equation with linear diffusion and super-linear drift introduced by Kaniadakis and Quarati [11, 12] to describe the evolution of a gas of Bose-Einstein particles. For kinetic equation of this type it is well-known that, in the physical space R3, the structure of the equilibrium Bose-Einstein distribution depends upon a parameter m∗, the critical mass. We are able to des...

Abstract. A thermal squeezed state representation of inflaton is constructed for a flat Friedmann-Robertson-Walker background metric and the phenomenon of particle creation is examined during the oscillatory phase of inflaton, in the semiclassical theory of gravity. An approximate solution to the semiclassical Einstein equation is obtained in thermal squeezed state formalism by perturbatively a...

abstract The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affine Lie algebra) of the WZW model, while the Einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal fiel...

We consider the Einstein-dust equations with positive cosmological constant λ on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold S. It is shown that the set of standard Cauchy data for the Einstein-λ-dust equations on S contains an open (in terms of suitable Sobolev norms) subset of data that develop into solutions which admit at future time-like infinity a space-l...