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Starting from the stationary cylindrically symmetric solution, but with the coordinates z and ϕ interchanged, and supposing that it could describe the vacuum spacetime of a translating cylinder, we investigate its physical and geometrical properties. This hypothesis is not entirely new since it has already been considered in a previous paper descri...
With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of general relativity. In particular, we first review the general properties, both local and global, of several import...
Starting from the stationary cylindrically symmetric solution, but with the coordinates $z$ and $\phi$ interchanged, and supposing that it could describe the vacuum spacetime of a translating cylinder, we investigate its physical and geometrical properties. This hypothesis is not entirely new since it has already been considered in a previous paper...
We investigate a class of cylindrically symmetric inhomogeneous $\Lambda$-dust spacetimes which have a regular axis and some zero expansion component. For $\Lambda\ne 0$, we obtain new exact solutions to the Einstein equations and show that they are unique, within that class. For $\Lambda=0$, we recover the Senovilla-Vera metric and show that it ca...
In the framework of a model based on the gravitational field of the Kerr black hole, we turn to analyse the kinematic behaviour of extragalactic jets. We analytically calculate the observable velocities and accelerations along any geodesic. Then, by numerical calculations, we apply our results to a geodesic, typical of the M87 jet, and we probe our...
We analyse the geodesics' dynamics in cylindrically symmetric vacuum spacetimes with Lambda>0 and compare it to the Lambda=0 and Lambda<0 cases. When Lambda>0 there are two singularities in the metric which brings new qualitative features to the dynamics. We find that Lambda=0 planar timelike confined geodesics are unstable against the introduction...
In the framework of a model based on the gravitational field of the Kerr black hole, we turn to investigate the kinematic behavior of extragalactic jets. We analytically calculate the observable velocities and accelerations along any geodesic. Then, by numerical calculations, we apply our results to a geodesic, typical of the M87 jet, and probe our...
We present here the general expressions for the acceleration of massive test
particles along the symmetry axis of the Kerr metric, and then study the main
properties of this acceleration in different regions of the spacetime. In
particular, we show that there exists a region near the black hole in which the
gravitational field is repulsive. We prov...
We present here the general expressions for the acceleration of massive test particles along the symmetry axis of the Kerr metric, and then study the main properties of this acceleration in different regions of the spacetime. In particular, we show that there exists a region near the black hole in which the gravitational field is repulsive. We prov...
We analyse the geodesics' dynamics in cylindrically symmetric vacuum spacetimes with Λ > 0 and compare it to the Λ = 0 and Λ > 0 cases. When Λ > 0 there are two singularities in the metric which brings new qualitative features to the dynamics. We find that Λ = 0 planar timelike confined geodesics are unstable against the introduction of a sufficien...
We present a comparative study about the dynamics of geodesic orbits in static cylindrically symmetric vacuum spacetimes with and without a cosmological constant.. In particular, we analyze the orbital stability of the Lambda = 0 case with respect to the introduction of arbitrarily small values of vertical bar Lambda vertical bar and single out the...
We consider static conformally flat cylindrically symmetric spacetimes with a cosmological constant and study the matching problem with the exterior Linet-Tian spacetime. We show that the matching is impossible if Λ < 0.
Particle collisions in black hole ergoregions may result in extremely high
center of mass energies that could probe new physics if escape to infinity were
possible. Here we show that some geodesics at high inclinations to the
equatorial plane may be unbound. Hence a finite flux of annihilation debris is
able to escape, especially in the case of nea...
We investigate the geodesics’ kinematics and dynamics in the Linet–Tian metric with [TEX equation: \Lambda Keywords: Cylindrically symmetric spacetimes; Exact solutions; General relativity; Geodesics; Stability Document Type: Research Article DOI: http://dx.doi.org/10.1007/s10714-014-1681-7 Affiliations: 1: Centro de Matemática, Universidade do Min...
Assuming that the spin $a$ of the black hole, presumably located at the core
of the active galactic nuclei Messier 87 (M87), takes the value which maximises
the ergospheric volume of the Kerr spacetime, we find results compatible with
the recent observations obtained by high resolution interferometry on the
origin of the jet, which would be located...
We investigate the matching, across cylindrical surfaces, of static cylindrically symmetric conformally flat spacetimes with a cosmological constant Λ, satisfying regularity conditions at the axis, to an exterior Linet-Tian spacetime [B. Linet, J. Math. Phys. 27, 1817–1818 (1986; Zbl 0593.53040)]. We prove that for Λ≤0 such matching is impossible....
Observations suggest that relativistic particles play a fundamental role in
the dynamics of jets emerging from active galactic nuclei as well as in their
interaction with the intracluster medium. However, no general consensus exists
concerning the acceleration mechanism of those high energy particles. A
gravitational acceleration mechanism is here...
Geodesics are studied in the spacetime described by the γ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry.
We consider spherically symmetric distributions of anisotropic fluids with a
central vacuum cavity, evolving under the condition of vanishing expansion
scalar. Some analytical solutions are found satisfying Darmois junction
conditions on both delimiting boundary surfaces, while some others require the
presence of thin shells on either (or both) bou...
The total energy in a sphere containing an isotropic shear-free conducting heat fluid is studied in the frame of a spherically symmetric metric. Firstly, we examine the role played by the heat flux. Secondly, we point out the contribution to the energy by the Weyl tensor. We obtain different formulas for the total energy, and those formulas are sho...
The increasing data set of precise observations of very energetic and collimated jets, with black hole (BH) as putative central engine, at different astrophysical scales and in various environments, should soon permit to discriminate and classify current theoretical models able to describe the jets formation. We construct a purely gravitational the...
We study the dynamical instability of a spherically symmetric anisotropic
fluid which collapses adiabatically under the condition of vanishing expansion
scalar. The Newtonian and post Newtonian regimes are considered in detail. It
is shown that within those two approximations the adiabatic index $\Gamma_1$,
measuring the fluid stiffness, does not p...
We consider the evolution of cavities within spherically symmetric
relativistic fluids, under the assumption that proper radial distance between
neighboring fluid elements remains constant during their evolution (purely
areal evolution condition). The general formalism is deployed and solutions are
presented. Some of them satisfy Darmois conditions...
In this paper, we present a systematical study of braneworlds of string theory on S¹/Z2. In particular, starting with the toroidal compactification of the Neveu–Schwarz/Neveu–Schwarz sector in D + d dimensions, we first obtain an effective D-dimensional action, and then compactify one of the D - 1 spatial dimensions by introducing two orbifold bran...
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...
We study the dynamical instability of a spherically symmetric anisotropic
fluid which collapses adiabatically under the condition of vanishing expansion
scalar. The Newtonian and post Newtonian regimes are considered in detail. It
is shown that within those two approximations the adiabatic index $\Gamma_1$,
measuring the fluid stiffness, does not p...
In general relativity, the gravitational field of an infinite rotating
cylinder is globally (but not locally) different from that of a static
cylinder. It is shown here that, for an infinite rigidly translating
(non-rotating) cylinder of perfect fluid with a regular axis, there
exists a (translating) frame of reference relative to which the
gravita...
We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all models are necessarily geodesic and a subclass of the Lemaitre-Tolman-Bondi solution is obtained. In the dissipati...
In a recent paper a systematic study on shearing expansion-free spherically
symmetric distributions was presented. As a particular case of such systems,
the Skripkin model was mentioned, which corresponds to a nondissipative perfect
fluid with a constant energy density. Here we show that such a model is
inconsistent with junction conditions. It is...
We consider diagonal cylindrically symmetric metrics, with an interior representing a general non-rotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions. We show that the matching conditions can be explicitly solved for the boundary values of metric components and...
Recently, in Gong et al (2008 Phys. Lett. B 663 147 [arXiv:0711.1597]) and Wang and Santos (2007 arXiv:0712.3938) we showed that the effective cosmological constant on each of the two orbifold branes can be easily lowered to its current observational value, by using the large extra dimensions in the framework of both M-theory and string theory on S...
We present a systematical study of brane worlds in string theory on $S^{1}/Z_{2}$. Starting with the toroidal compactification of the NS/NS sector in (D+d) dimensions, we first obtain an effective $D$-dimensional action, and then compactify one of the $(D-1)$ spatial dimensions by introducing two orbifold branes as its boundaries. By combining the...
Dynamical models of prototype gravastars were constructed in order to study
their stability. The models are the Visser-Wiltshire three-layer gravastars, in
which an infinitely thin spherical shell of stiff fluid divides the whole
spacetime into two regions, where the internal region is de Sitter, and the
external is Schwarzschild. It is found that...
We extend the method of separation of variables, studied by B. Léauté and G. Marcilhacy [Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 31, 363–375 (1979; Zbl 0449.35088)], to obtain transcendent solutions of the field equations for stationary axisymmetric systems. These solutions depend on transcendent functions satisfying a third order differenti...
Orbifold branes in string theory are investigated, and the general field equations both outside and on the branes are given explicitly for type II and heterotic string. The radion stability is studied using the Goldberger–Wise mechanism, and shown explicitly that it is stable. It is also found that the effective cosmological constant on each of the...
We present a complete set of the equations and matching conditions required for the description of physically meaningful charged, dissipative, spherically symmetric gravitational collapse with shear. Dissipation is described with both free-streaming and diffusion approximations. The effects of viscosity are also taken into account. The roles of dif...
We re-examine the possibility that astrophysical jet collimation may arise from the geometry of rotating black holes and the presence of high-energy particles resulting from a Penrose process, without the help of magnetic fields. Our analysis uses the Weyl coordinates, which are revealed better adapted to the desired shape of the jets. We numerical...
We review the matching conditions for a collapsing anisotropic cylindrical perfect fluid, recently discussed in the literature (2005 {\it Class. Quantum Grav.} {\bf 22} 2407). It is shown that radial pressure vanishes on the surface of the cylinder, contrary to what is asserted in that reference. The origin of this discrepancy is to be found in a m...
We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful stationary cylindrically symmmetric distributions of matter, smoothly matched to Lewis vacuum spacetime. A specific example is given. The electric and magnetic parts of the Weyl tensor are calculated, and it is shown t...
Five-dimensional spacetimes of two orbifold 3-branes are studied, by assuming that the two 3-branes are spatially homogeneous, isotropic, and independent of time, following the so-called “bulk-based” approach. The most general form of the metric is obtained, and the corresponding field equations are divided into three groups, one is valid on each o...
A study covering some aspects of the Einstein--Rosen metric is presented. The electric and magnetic parts of the Weyl tensor are calculated. It is shown that there are no purely magnetic E--R spacetimes, and also that a purely electric E--R spacetime is necessarily static. The geodesics equations are found and circular ones are analyzed in detail....
Without making use of the Ernst formalism we look directly for particular solutions of field equations describing stationary axisymmetric vacuum space–time using Weyl coordinates. The solutions that we obtain, by simple separation of variables, are parametrized in the general case by a III transcendent of Painleve´ with two arbitrary constants.
The electric and the magnetic part of the Weyl tensor, as well as the invariants obtained from them, are calculated for the Bondi vacuum metric. One of the invariants vanishes identically and the other only exhibits contributions from terms of the Weyl tensor containing the static part of the field. It is shown that the necessary and sufficient con...
The full text of this article is available in the PDF provided.
This corrigendum has been prepared jointly by the original authors (L Herrera and N O Santos) and M A H MacCallum
We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful static cylindrically symmmetric distributions of matter, smoothly matched to Levi-Civita vacuum spacetime. It is shown that the conformally flat solution with equal principal stresses represents an incompressible fluid...
The Misner and Sharp approach to the study of gravitational collapse is extended to the dissipative case in, both, the streaming out and the diffusion approximations. The role of different terms in the dynamical equation are analyzed in detail. The dynamical equation is then coupled to a causal transport equation in the context of Israel--Stewart t...
The dragging of the Kerr-NUT solution does not tend to zero at infinity. To modify this solution in order to produce a good asymptotic behaviour we transform it by introducing two further parameters with the aid of a SU(1,1) transformation followed by a unitary transformation. By imposing a certain relation between these parameters we obtain a new...
The full set of equations governing the evolution of self--gravitating
spherically symmetric dissipative fluids with anisotropic stresses is deployed
and used to carry out a general study on the behaviour of such systems, in the
context of general relativity. Emphasis is given to the link between the Weyl
tensor, the shear tensor, the anisotropy of...
Here we study some general properties of spherical shear-free collapse. Its general solution when imposing conformal flatness is reobtained [1,2] and matched to the outgoing Vaidya spacetime. We propose a simple model satisfying these conditions and study its physical consequences. Special attention deserve, the role played by relaxational processe...
Topological charged black holes coupled with a cosmological constant in $R^{2}\times X^{D-2}$ spacetimes are studied, where $X^{D-2}$ is an Einstein space of the form ${}^{(D-2)}R_{AB} = k(D-3) h_{AB}$. The global structure for the four-dimensional spacetimes with $k = 0$ is investigated systematically. The most general solutions that represent a T...
Topological charged black holes coupled with a cosmological constant in $R^{2}\times X^{D-2}$ spacetimes are studied, where $X^{D-2}$ is an Einstein space of the form ${}^{(D-2)}R_{AB} = k(D-3) h_{AB}$. The global structure for the four-dimensional spacetimes with $k = 0$ is investigated systematically. The most general solutions that represent a T...
We analyse the concept of active gravitational mass for Reissner-Nordstrom spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Ca...
The shear-free condition is studied for dissipative relativistic self-gravitating fluids in the quasi-static approximation.
It is shown that, in the Newtonian limit, such a condition implies the linear homology law for the velocity of a fluid element,
only if homology conditions are further imposed on the temperature and the emission rate. It is al...
We revisit axisymmetric stationary vacuum solutions of the Einstein equations, like we did for the cylindrical case [J. Math. Phys. 41, 7535 (2000)]. We explicitly formulate the simplest hypothesis under which the S(A) solutions, or axisymmetric Lewis solutions can be found and demonstrate that this hypothesis leads to a linear relation between the...
We analyse the concept of active gravitational mass for Reissner-Nordstrom
spacetime in terms of scalar polynomial invariants and the Karlhede
classification. We show that while the Kretschmann scalar does not produce the
expected expression for the active gravitational mass, both scalar polynomial
invariants formed from the Weyl tensor, and the Ca...
From the Kerr solution of Ernst equation under Ehlers and unitary transformations, we build a parametrized Kerr solution depending on three parameters, namely the mass, the angular momentum of the source and an adimensional parameter m
1. Varying m
1 produces a topological deformation of the ergosphere.
We derive the Teixeira, Wolk and Som method,1 for obtaining
electrostatic solutions from some given vacuum solutions, in its inverse
form. Then we use it to obtain the geometrical mass MS in the
Schwarzschild spacetime, and we find MS2=M^2-Q^2,
where M and Q are, respectively, the mass and charge parameters of the
Reissner-Nordström spacetime. We c...
Rotating thin-shell-like sources for the stationary cylindrically symmetric vacuum solutions (Lewis) are constructed and studied. It is found, by imposing the non existence of timelike curves in the exterior of the shell, and that the source satisfies the weak, dominant and strong energy conditions that the parameters, commonly denoted by $a$ and $...
Using Ehlers and unitary transformations, from Bonanos solution of the Ernst equation, we build a new vacuum stationary axisymmetric solution of Einstein equations depending on three parameters. The parameters are associated with the total mass of the source and its angular momentum. The third parameter produces a topological deformation of the erg...
We derive the Teixeira, Wolk and Som method, for obtaining electrostatic solutions from given vacuum solutions, in its inverse form. Then we use it to obtain the geometrical mass $M_S$ in the Schwarzschild spacetime, and we find $M_S^2=M^2-Q^2$, where $M$ and $Q$ are, respectively, the mass and charge parameters of the Reissner-Nordstr\"om spacetim...
A general iterative method proposed some years ago for the description of
relativistic collapse, is presented here in comoving coordinates. For doing
that we redefine the basic concepts required for the implementation of the
method for comoving coordinates. In particular the definition of the
post-quasistatic approximation in comoving coordinates i...
We apply the Euclidon method 1], for generating axisymmetric stationary so-lutions of Einstein's equations, to four static solutions with Newtonian potential describing semi-innnite line mass with linear mass density 1/2. The new solutions thus obtained are either the extreme Kerr black hole or the Kerr black hole.
We study the Levi-Civita metric for values of its σ parameter in the
range 0≤σ<∞. We show that the value σ = ½
makes the axial and angular coordinates switch meaning. We present its
geodesics and a physical source satisfying the energy conditions for
the entire range of σ. This source allows us to obtain an energy per
unit length which agrees with...
Using gyroscopes we generalize results, obtained for the gravitomagnetic clock effect in the particular case when the exterior spacetime is produced by a rotating dust cylinder, to the case when the vacuum spacetime is described by the general cylindrically symmetric Lewis spacetime. Results are contrasted with those obtained for the Kerr spacetime...
The local and global properties of the Levi-Civita (LC) solutions coupled with an electromagnetic field are studied and some limits to the vacuum LC solutions are given. By doing such limits, the physical and geometrical interpretations of the free parameters involved in the solutions are made clear. Sources for both the LC vacuum solutions and the...
The physical meaning of the Levi-Civita spacetime, for some "critical" values of the parameter s, is discussed in the light of gedanken experiments performed with gyroscopes circumscribing the axis of symmetry. The fact that s = 1/2 corresponds to flat space described from the point of view of an accelerated frame of reference, led us to incorporat...
We propose a new presentation of the Demia\'{n}ski-Newman (DN) solution of the axisymmetric Einstein equations. We introduce new dimensionless parameters $p$, $q$ and $s$, but keeping the Boyer-Lindquist coordinate transformation used for the Kerr metric in the Ernst method. The family of DN metrics is studied and it is shown that the main role of...
We show how to reobtain the Kerr and Schwarzschild solutions from a particular Lewis static solution.
Geodesics are studied in the spacetime described by the γ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry.
We revisit Lewis solution giving a mechanical interpretation to its field equations. The structure of the equations that the metric coefficients satisfy can be associated to the motion of a classical particle in a central field.
We present calculations of gyroscope precession in spacetimes described by Levi-Civita and Lewis metrics, under different circumstances. By doing so we are able to establish a link between the parameters of the metrics and observable quantities, providing thereby a physical interpretation for those parameters, without specifying the source of the f...
The main properties of the Levi-Cività solutions with a cosmological constant are studied. In particular, it is found that some of the solutions need to be extended beyond certain hypersurfaces in order to have geodesically complete spacetimes. Some extensions are considered and found to give rise to a black hole structure but with plane symmetry....
We discuss gravitomagnetism in connection with rotating cylindrical systems. In particular, the gravitomagnetic clock effect is investigated for the exterior vacuum field of an infinite rotating cylinder. The dependence of the clock effect on the parameters of the stationary Lewis metric is determined. We illustrate our results by means of the van...
The main properties of the Levi-Civita solutions with the cosmological constant are studied. In particular, it is found that some of the solutions need to be extended beyond certain hypersurfaces in order to have geodesically complete spacetimes. Some extensions are considered and found to give rise to black hole structure but with plane symmetry....
In the framework of a spatially flat FLRW model, we account for dissipative effects in a simple fluid, namely bulk viscosity and matter creation. For an isentropic evolution, we study the wavefront speeds associated with the characteristics of the fluid. With the assumption of a barotropic equation of state, we investigate the consequences on these...
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries
83C75 Space-time singularities, cosmic censorship, etc.
We match the vacuum, stationary, cylindrically symmetric solution of Einstein's field equations with , in a form recently given by Santos, as an exterior to an infinite cylinder of dust cut out of a Gödel universe. There are three cases, depending on the radius of the cylinder. Closed timelike curves are present in the exteriors of some of the solu...
The cosmological equations for the general scalar tensor theory proposed by Nordvedt (1970) in a Bianchi type-I radiation-filled Universe are solved and the behaviour of the model is discussed. There are two distinct situations. Either the Universe will explode from a bit band type singularity and continuously increase, or the Universe may continuo...
The authors study the role played by local anisotropy in the onset of dynamical instabilities in self-gravitating systems. They determine that small anisotropies in the unperturbed system can drastically change its stability. Some speculations and prospective applications to astrophysical scenarios are suggested.
For a static dust distribution charged in both the electric and scalar sense the authors prove that the sum of squares of these two types of charge densities must be either greater than or equal to the square of the mass density, when the scalar potential is a function of the electrostatic potential. In the absence of either the electrical or scala...
The authors consider spacetimes of general relativity admitting a preferred null direction lmu and a two-dimensional Abelian group of isometries G2. A null tetrad formulation of the Killing equations is given, as well as a classification of G2 according to the orientation of lmu with respect to the group transitivity surfaces. Two theorems concerni...
A solution to the Einstein-Dirac system of equations in a Robertson-Walker spacetime is presented using the separation of variables method. With an axially symmetric and a non-axially symmetric boundary conditions, we find that there are no solutions for the massless fermions and only null or `ghost' solutions for the massive fermions. The `ghost'...
The Wright and Lanczos solutions are studied, which represent the gravitational field produced by a rigidly rotating dust cylinder coupled with the cosmological constant. It is shown that when certain physical conditions are imposed the five-parameter Wright solutions reduce to the two-parameter Lanczos solutions. The geodesic motion of test partic...
The spherical gravitational collapse of a compact packet consisting of perfect fluid is studied. The spacetime outside the packet is described by the out-going Vaidya radiation fluid. It is found that when the collapse has continuous self-similarity the formation of black holes always starts with zero mass, and when the collapse has no self-similar...
It is shown that the Levi-Civita metric can be obtained from a family of the Weyl metric, the Gamma metric, by taking the limit when the length of its Newtonian image source tends to infinity. In this process a relationship appears between two fundamental parameters of both metrics. Comment: LaTeX2e 17 pages
We study the fate of gravitational collapse in presence of a cosmological constant. The junctions conditions between static and non-static space-times are deduced. Three apparent horizon are formed, but only two have physical significance, one of them being the black hole horizon and the other the cosmological horizon. The cosmological constant ter...
We discuss gravitomagnetism in connection with rotating cylindrical systems. In particular, the gravitomagnetic clock effect is investigated for the exterior vacuum field of an infinite rotating cylinder. The dependence of the clock effect on the Weyl parameters of the stationary Lewis metric is determined. We illustrate our results by means of the...
The derivation of the general solutions for stationary and static cylindrically symmetric Einstein spaces of Lewis form is revisited and the physical and geometrical meaning of the parameters appearing in the resulting solutions are investigated. It is shown that three of the parameters (and the value of the cosmological constant) are essential, of...
We obtain an expression for the active gravitational mass of a collapsing fluid distribution, which brings out the role of density inhomogeneity and local anisotropy in the fate of spherical collapse. Comment: 13 pages in Latex, to appear in Physics Letters A
On p 2402 the third term on the right-hand side of equation (9) should have k' instead of k'2.
On p 2403 the following equations should be modified to
on p 2404 to
on p 2405 to
and on p 2406 to
We review and discuss possible causes for the appearance of local anisotropy (principal stresses unequal) in self-gravitating systems and present its main consequences. We consider both Newtonian and general relativistic examples. The results emerging from the stability analysis hint at the potential relevance of local anisotropy in the evolution o...
The static vacuum plane spacetimes are considered, which have two non-trivial solutions: The Taub solution and the Rindler solution. Imposed reflection symmetry, we find that the source for the Taub solution does not satisfy any energy conditions, which is consistent with previous studies, while the source for the Rindler solution satisfies the wea...
We consider a conformally flat, inhomogeneous solution of the Einstein equations for a dissipative fluid. The production of
entropy is found to depend on some arbitrary functions of time. By some subsidiary conditions, such a model is shown to evolve
into a homogeneous Friedmann-type universe.
The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force parallel to the axial axis and without Newtonian analogue. Comment: 15 pages, Latex