We provide the exact time-dependent cosmological solutions in the RandallSundrum (RS) setup with bulk matter, which may be smoothly connected to the static RS metric. In the static limit of the extra dimension, the solutions are reduced to the standard Friedmann equations. In view of our solutions, we also propose an explanation for how the extra dimension is stabilized in spite of a flat modul...

We look for solutions in Einstein gravity corresponding to inflating braneworlds of arbitrary dimension and co-dimension. These solutions correspond to isolated sources (no long range fields). Using dynamical systems techniques, we show that there exists a unique solution corresponding to a black p-brane with a regular horizon at the location of the brane. The solution is not however asymptotic...

We show uniqueness results for the Dirichlet problem for YangMills connections defined in n-dimensional (n ≥ 4) star-shaped domains with flat boundary values. This result also shows the non-existence result for the Dirichlet problem in dimension 4, since in 4-dimension, there exist countably many connected components of connections with prescribed Dirichlet boundary value. We also show non-exis...

Given a presentation of a finitely presented group, there is a natural way to represent the group as the fundamental group of a 2-complex. The first part of this paper demonstrates one possible way to represent a finitely presented algebra S in a similarly compact form. From a presentation of the algebra, we construct a quiver with relations whose path algebra is finite dimensional. When we adj...

We study the impact of classical short-range nonlinear interactions on transport in lattices with no dispersion. The single particle band structure these contains flat bands only, and cages non-interacting particles into compact localized eigenstates. demonstrate that there always exist local unitary transformations detangle such decoupled sites dimension one. Starting from a detangled represen...

We start from a hyperbolic DN hydrodynamic type system of dimension n which possesses Riemann invariants and we settle the necessary conditions on the conservation laws in the reciprocal transformation so that, after such a transformation of the independent variables, one of the metrics associated to the initial system be flat. We prove the following statement: let n ≥ 3 in the case of reciproc...

Given a presentation of a finitely presented group, there is a natural way to represent the group as the fundamental group of a 2-complex. The first part of this paper demonstrates one possible way to represent a finitely presented algebra S in a similarly compact form. From a presentation of the algebra, we construct a quiver with relations whose path algebra is finite dimensional. When we adj...

A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...

We present a non-singular instanton describing the creation of an open universe with a compactified extra dimension. The four dimensional section of this solution is a singular instanton of the type introduced by Hawking and Turok. The “singularity” is viewed in five dimensions as a smooth bubble of “nothing” which eats up a portion of spacetime as it expands. Flat space with a compact extra di...

A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...