3 research outputs found
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
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