Solutions of Kramer's Equations for Perfect Fluid Cylinders

Kramer's formulation of Einstein's fieldequations for static perfect fluid cylinders isconsidered. Three approaches are followed in seekingsolutions of Kramer's equations. First, a particularintegral is found which reproduces a previously knownclass of four solutions. Second, a fairly general ansatzis suggested, whereby a class of six new solutions isderived. Finally, the problem for an incompressible perfect fluid, with constant energy density, isreduced to a single second order equation. All solutionsare regular everywhere. Constraints are imposed on thesolutions parameters such that energy conditions are satisfied and hence the solutions arephysically reasonable.     

Lie Groups of Conformal Motions Acting on Null Orbits

Space-times admitting a 3-dimensional Lie group of conformal motions acting on null orbits containing a 2-dimensional Abelian subgroup of isometries are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespective of the matter content) and then all possible perfect fluid solutions are found, although none of these verify the weak and dominant energy conditions over the whole space-time manifold.     

Fluid phase equilibrium studies on model substances for supercritical fluid extraction with CO2 up to 100 MPa

Abstract

Multicomponent fluid phase equilibrium data are of increasing interest for applications in Supercritical Fluid Extraction (SFE) where compressed supercritical gases are used for the extraction of low-volatile substances (e.g. caffeine from coffee and tea, hops etc.). Sometimes so-called moderator substances have to be added in order to increase solvent power and/or selectivity. Systematic measurements on a four-component system of the type CO₂ + fatty alcohol (e.g. 1-do-decanol) + alkane (e.g. hexadecane) as a function of the amount of moderator added were performed at 393 K and at pressures from 10 to 100 MPa in an analytical high-pressure cell. Separation factors calculated from the p,T,w/,w, “data are presented and discussed.     

Quantum Mixtures in the Early Universe

In Relativistic Schrödinger Theory for spinning matter, there exist mixtures which have vanishing spin density (S 0). Such a fermionic, but spinless quantum fluid is studied in detail. Its energy-momentum density can develop negative pressure which is able to accelerate the expansion of the universe and to create matter energy through continuous bouncing at minimal radius (cosmic pumping).     

General-Relativistic Thomas-Fermi Model

A system of self-gravitating massive fermions isstudied in the framework of the general-relativisticThomas-Fermi model. We study the properties of the freeenergy functional and its relation to Einstein's fleld equations. We then describe aself-gravitating fermion gas by a set of Thomas-Fermitype self-consistency equations.     

Einstein-Fokker-Planck Equation for a Collapsing Perfect Fluid Star in a Thermal Noise Bath: Static Thermal Black Hole as the Equilibrium Solution

This paper considers sphericalOppenheimer-Snyder gravitational collapse of dust orperfect fluid stars immersed within aspacetime containing a thermal bath of (Gaussian) whitenoise at a temperature T, obeying the autocorrelations of thefluctation-dissipation theorem. Candidates for theresulting non-linear Einstein-Langevin (EL) stochasticdifferential field equations are developed. A collapsing fluid or dust star coupled to the stochastic,external thermal bath of fluctuations is theninterpreted as an example of a non-linear, noisy system,somewhat analogous to a non-linear Brownian motion in a viscous, thermal bath at temperature T. AnEinstein-Fokker-Planck (EFP) hydrodynamical continuityequation, describing the collapse as a probability flowwith respect to the exterior standard time t_s outside the collapsing body, is developed. Thethermal equilibrium or stationary solution can bederived in the infinite standard time relaxation limit.This limit (t_s ) only exists for a static, external observer within thenoise bath viewing the collapsing sphere such that R 1 (the event horizon) with unit probability ast_s . The stationary or thermalequilibrium solution of the efp equations therefore seemsto correspond to a static black hole in a Hartle-Hawkingstate at the Hawking temperature t_H. The OSmodel first predicted event horizons and singularities. It is interesting that through a simplestochastic extension of the model, one can conclude thatthe final collapsed, static, equilibrium state of thebody must be a thermal black hole at the Hawkingtemperature.     

Evolution of Thin-wall Configurations ofTexture Matter

We consider the matter of global textures withinthe frameworks of a perfect fluid model in generalrelativity. We examine thermodynamical properties oftexture matter in comparison with radiation fluid and bubble matter. Then we study dynamics ofthin-wall selfgravitating texture objects, and show thatclassical motion can be elliptical (finite), parabolicalor hyperbolical. It is shown that total gravitational mass of neutral textures in equilibrium equalszero, as was expected. Finally, we carry out theWheeler-DeWitt minisuperspace quantization of thetheory, obtain exact wave functions and discrete spectra of bound states with provision for spatialtopology.     

Perfect Fluid Spacetimes with a Purely Magnetic Weyl Tensor

We present a solution of the gravitational fieldequations which is similar in form to that given byWainwright. Several cases are considered, in particularwe find a general algebraic perfect fluid solution with equation of state p = whose Weyl tensor is of the purely magnetic type within a finiteregion of the spacetime. It is shown, for an observerwith four-velocity, u_mag say, that themetric's Weyl tensor is purely magnetic within the finiteregion while it is purely electric, as read by anotherobserver with four-velocity u_ele, elsewhere.Another observer, independent of the observers whomeasure the Weyl tensor to be purely electric ormagnetic, interprets the perfect fluid to have anequation of state p = . The Petrov type of themetric, in this case, is I(M) by theArianrhod-McIntosh classification and therefore there exists noconformally related metric which is vacuum. The vacuumseed metrics are derived for the perfect fluidsolutions.     

Theorems on Shear-Free Perfect Fluids with Their Newtonian Analogues

In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the simpler case of vanishing acceleration) must be either non-expanding or non-rotating. We also show that these results are not necessarily true in the Newtonian case, and present an explicit comparison of shear-free dust in Newtonian and relativistic theories in order to see where and why the differences appear.     

Cracking of Homogeneous Self-Gravitating Compact Objects Induced by Fluctuations of Local Anisotropy

We discuss the effect that small fluctuations of local anisotropy (principal stresses unequal) may have on the occurrence of cracking in spherical compact objects. Two families of homogeneous fluid distributions are considered. For both it is shown that departures from equilibrium may lead to the appearance of cracking, only if fluctuations of local anisotropy are allowed. The case of fluctuations in an initially locally isotropic (perfect fluid) configuration deserves particular attention.