Related papers: Embedding of the Brane into Six Dimensions
We address the question of cosmological perturbations in the context of brane cosmology, where our Universe is a three-brane where matter is confined, whereas gravity lives in a higher dimensional spacetime. The equations governing the bulk…
We study the geometrical and topological properties of the bulk (environment space) when we modify the geometry or topology of a brane-world. Through the characterization of a spherically symmetric space-time as a local brane-world immersed…
We discuss cosmological models in six-dimensional spacetime. For codimension-1 branes, we consider a (4+1) braneworld model and discuss its cosmological evolution. For codimension-2 branes, we consider an infinitely thin conical braneword…
It is shown that the gauge theory of relativistic 3-Branes can be formulated in a conformally invariant way if the embedding space is six-dimensional. The implementation of conformal invariance requires the use of a modified measure,…
Five-dimensional scenarios with infinitesimally thin branes replaced by appropriate configurations of a scalar field were considered. A possibility of periodic extra dimension was discussed in the presence on non-minimal scalar-gravity…
We consider the cosmology of a ``3-brane universe'' in a five dimensional (bulk) space-time with a cosmological constant. We show that Einstein's equations admit a first integral, analogous to the first Friedmann equation, which governs the…
The group-theoretic method for constructing symmetric isometric embeddings is used to describe all possible four-dimensional surfaces in flat $(1,9)$-dimensional space, whose induced metric is static and spherically symmetric. For such…
We consider branes as "points" in an infinite dimensional brane space ${\cal M}$ with a prescribed metric. Branes move along the geodesics of ${\cal M}$. For a particular choice of metric the equations of motion are equivalent to the well…
We constructed a six-dimensional version of the standing wave model with an anisotropic 4-brane generated by a phantom-like scalar field. The model represents a braneworld where the compact (on-brane) dimension is assumed to be sufficiently…
I develop the idea that our world is a brane-like object embedded in Euclidean bulk. In its ground state, the brane constituent matter is assumed to be homogeneous and isotropic, and of negligible influence on the bulk geometry. The…
The question how an $M$-dimensional extended object must be shaped so that a rigid motion gives an $M$-brane solution ($M+1$ dimensional timelike zero mean curvature surface) in $M+2$ dimensional Minkowski space is discussed for closed…
We consider a recently proposed setup where a codimension one brane is embedded in the background of a smooth domain wall interpolating between AdS and Minkowski minima. Since the volume of the transverse dimension is infinite, bulk…
We suggest a mechanism by which four-dimensional Newtonian gravity emerges on a 3-brane in 5D Minkowski space with an infinite size extra dimension. The worldvolume theory gives rise to the correct 4D potential at short distances whereas at…
We review and further analyze Penrose's 'light cone at infinity' - the conformal closure of Minkowski space. Examples of a potential confusion in the existing literature about it's geometry and shape are pointed out. It is argued that it is…
We consider ``cosmologically symmetric'' (i.e. solutions with homogeneity and isotropy along three spatial dimensions) five-dimensional spacetimes with a scalar field and a three-brane representing our universe. We write Einstein's…
I show that all FRW models (four dimensional pseudo-Riemannian manifolds with maximally symmetric space) can be embedded in a flat Minkowski manifold with 5 dimensions. The pseudo Riemannian metric of space-time is induced by the flat…
The global geometries of bulk vacuum space-times in the brane-universe models are investigated and classified in terms of geometrical invariants. The corresponding Carter-Penrose diagrams and embedding diagrams are constructed. It is shown…
We consider cosmological models where the universe, governed by Einstein's equations, is a piece of a five dimensional double-sided anti-de Sitter spacetime (that is, a "$Z_2$-symmetric bulk") with matter confined to its four dimensional…
Motivated by the holographic self-tuning proposal of the cosmological constant, we generalize and study the cosmology of brane-worlds embedded in a higher-dimensional bulk black hole geometry. We describe the equations and matching…
We consider a five-dimensional brane world scenario where the fifth dimension is compactified on $S^1/Z_2$. We show that the familiar four-dimensional cosmology on our brane is easily recovered during a primordial stage of inflation if…