560 research outputs found
Riemann-Cartan Space-times of G\"odel Type
A class of Riemann-Cartan G\"odel-type space-times are examined in the light
of the equivalence problem techniques. The conditions for local space-time
homogeneity are derived, generalizing previous works on Riemannian G\"odel-type
space-times. The equivalence of Riemann-Cartan G\"odel-type space-times of this
class is studied. It is shown that they admit a five-dimensional group of
affine-isometries and are characterized by three essential parameters : identical triads () correspond to locally
equivalent manifolds. The algebraic types of the irreducible parts of the
curvature and torsion tensors are also presented.Comment: 24 pages, LaTeX fil
On rigidly rotating perfect fluid cylinders
The gravitational field of a rigidly rotating perfect fluid cylinder with
gamma- law equation of state is found analytically. The solution has two
parameters and is physically realistic for gamma in the interval (1.41,2].
Closed timelike curves always appear at large distances.Comment: 10 pages, Revtex (galley
Recommended from our members
Dilatometry in the Gleeble: What did you really measure?
The Gleeble is an oft-used tool for welding metallurgy research. Besides producing synthetic weld specimens, it is used to determine phase transformation temperatures and kinetics via dilatometry. Experimental data and an FEM model are used to examine measured dilatation errors because of non-uniform heating of the dilatometer and other sources such as sample elastic and plastic deformation. Both isothermal and constant heating/cooling rate scenarios are considered. Further errors which may be introduced when the dilatation is incorrectly assumed to be linearly related to the volume fraction transformed are also discussed
Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D
In this paper we derive homogeneous vacuum plane-wave solutions to Einstein's
field equations in 4+1 dimensions. The solutions come in five different types
of which three generalise the vacuum plane-wave solutions in 3+1 dimensions to
the 4+1 dimensional case. By doing a Kaluza-Klein reduction we obtain solutions
to the Einstein-Maxwell equations in 3+1 dimensions. The solutions generalise
the vacuum plane-wave spacetimes of Bianchi class B to the non-vacuum case and
describe spatially homogeneous spacetimes containing an extremely tilted fluid.
Also, using a similar reduction we obtain 3+1 dimensional solutions to the
Einstein equations with a scalar field.Comment: 16 pages, no figure
Einstein billiards and spatially homogeneous cosmological models
In this paper, we analyse the Einstein and Einstein-Maxwell billiards for all
spatially homogeneous cosmological models corresponding to 3 and 4 dimensional
real unimodular Lie algebras and provide the list of those models which are
chaotic in the Belinskii, Khalatnikov and Lifschitz (BKL) limit. Through the
billiard picture, we confirm that, in D=5 spacetime dimensions, chaos is
present if off-diagonal metric elements are kept: the finite volume billiards
can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody
algebras. The most generic cases bring in the same algebras as in the
inhomogeneous case, but other algebras appear through special initial
conditions.Comment: 27 pages, 10 figures, additional possibility analysed in section 4.3,
references added, typos correcte
Invariant construction of solutions to Einstein's field equations - LRS perfect fluids II
The properties of LRS class II perfect fluid space-times are analyzed using
the description of geometries in terms of the Riemann tensor and a finite
number of its covariant derivatives. In this manner it is straightforward to
obtain the plane and hyperbolic analogues to the spherical symmetric case. For
spherically symmetric static models the set of equations is reduced to the
Tolman-Oppenheimer-Volkoff equation only. Some new non-stationary and
inhomogeneous solutions with shear, expansion, and acceleration of the fluid
are presented. Among these are a class of temporally self-similar solutions
with equation of state given by , and a class of
solutions characterized by . We give an example of geometry
where the Riemann tensor and the Ricci rotation coefficients are not sufficient
to give a complete description of the geometry. Using an extension of the
method, we find the full metric in terms of curvature quantities.Comment: 24 pages, 1 figur
Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1
In this paper we classify all 4+1 cosmological models where the spatial
hypersurfaces are connected and simply connected homogeneous Riemannian
manifolds. These models come in two categories, multiply transitive and simply
transitive models. There are in all five different multiply transitive models
which cannot be considered as a special case of a simply transitive model. The
classification of simply transitive models, relies heavily upon the
classification of the four dimensional (real) Lie algebras. For the orthogonal
case, we derive all the equations of motion and give some examples of exact
solutions. Also the problem of how these models can be compactified in context
with the Kaluza-Klein mechanism, is addressed.Comment: 24 pages, no figures; Refs added, typos corrected. To appear in CQ
Nonadiabatic charged spherical gravitational collapse
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 different terms in the dynamical equation are
analyzed in detail. The dynamical equation is coupled to a causal transport
equation in the context of Israel-Stewart theory. The decrease of the inertial
mass density of the fluid, by a factor which depends on its internal
thermodynamic state, is reobtained, with the viscosity terms included. In
accordance with the equivalence principle, the same decrease factor is obtained
for the gravitational force term. The effect of the electric charge on the
relation between the Weyl tensor and the inhomogeneity of energy density is
discussed.Comment: 23 pages, Latex. To appear in Phys. Rev. D. Some references correcte
Structure and stability of the Lukash plane-wave spacetime
We study the vacuum, plane-wave Bianchi spacetimes described by
the Lukash metric. Combining covariant with orthonormal frame techniques, we
describe these models in terms of their irreducible kinematical and geometrical
quantities. This covariant description is used to study analytically the
response of the Lukash spacetime to linear perturbations. We find that the
stability of the vacuum solution depends crucially on the background shear
anisotropy. The stronger the deviation from the Hubble expansion, the more
likely the overall linear instability of the model. Our analysis addresses
rotational, shear and Weyl curvature perturbations and identifies conditions
sufficient for the linear growth of these distortions.Comment: Revised version, references added. To appear in Class. Quantum Gra
Stationary Cylindrical Anisotropic Fluid
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 that purely electric solutions are necessarily
static. Then, it is shown that no conformally flat stationary cylindrical fluid
exits, satisfying regularity and matching conditions.Comment: 17 pages Latex. To appear in Gen.Rel.Gra
- …