相关论文: Application of the Campbell-Magaard theorem to hig…

We extend Campbell-Magaard embedding theorem by proving that any n-dimensional semi-Riemannian manifold can be locally embedded in an (n+1)-dimensional Einstein space. We work out some examples of application of the theorem and discuss its…

We discuss and prove a theorem which asserts that any n-dimensional semi-Riemannian manifold can be locally embedded in a (n+1)-dimensional space with a non-degenerate Ricci tensor which is equal, up to a local analytic diffeomorphism, to…

A little known theorem due to Campbell is employed to establish the local embedding of a wide class of 4-dimensional spacetimes in 5-dimensional Ricci-flat spaces. An embedding for the class of n-dimensional Einstein spaces is also found.…

We investigate the embedding of four-dimensional branes in five-dimensional spaces. We firstly consider the case when the embedding space is a vacuum bulk whose energy-momentum tensor consists of a Dirac delta function with support in the…

According to the Campbell-Magaard theorem, any analytical spacetime can be locally and analytically embedded into a five-dimensional pseudo-Riemannian Ricci-flat manifold. We find explicitly this embedding for Godel's universe. The…

The extension of the Campbell-Magaard embedding theorem to general relativity with minimally-coupled scalar fields is formulated and proven. The result is applied to the case of a self-interacting scalar field for which new embeddings are…

The Campbell-Magaard theorem is widely seen as a way of embedding Einstein's 4D theory of general relativity in a 5D theory of the Kaluza-Klein type. We give a brief history of theorem, present a short account of it, and show that it…

We discuss how embeddings in connection with the Campbell-Magaard (CM) theorem can have a physical interpretation. We show that any embedding whose local existence is guaranteed by the CM theorem can be viewed as a result of the dynamical…

Various attempts to go beyond the theory of General Relativity start from the assumption that spacetime is not a 4-dimensional but rather a higher-dimensional manifold. Among others, braneworld scenarios postulate that the spacetime we…

We employ a theorem due to Campbell to build some simple 4-dimensional cosmological models which originate from solutions describing waves propagating along the extra-dimension of a 5-dimensional Ricci-flat space. The dimensional reduction…

We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl's geometry. We show that some of the known…

Here we present an overview of the work done over the years on the embedding of hypersurfaces in a space of higher dimension, with particular reference to the embedding of four-dimensional hypersurfaces in five-dimensional space-times. The…

In stark contrast with the three-dimensional case, higher-dimensional Chern-Simons theories can have non-topological, propagating degrees of freedom. Finding those vacua that allow for the propagation of linear perturbations, however,…

Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…

We investigate the possibility to recover a four-dimensional (4D) general theory of relativity, as embedded in a 5D spacetime where gravity is governed by a five-dimensional (5D) Brans-Dicke (BD) theory of gravity. Employing the…

The 5-dimensional (5d) Birkhoff theorem gives the class of 5d vacuum space-times containing spatial hypersurfaces with cosmological symmetries. This theorem is violated by the 5d vacuum Gergely-Maartens (GM) space-time, which is not a…

The proposed so far brane-world cosmological scenarios are concerned with (D-1)-dimensional embeddings into the D-dimensional spacetime, besides, it is supposed D=5 as a rule. However, it would be much more realistic to consider our…

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 braneworlds models were inspired partly by Kaluza-Klein's theory, where both the gravitational and the gauge fields are obtained from the geometry of a higher dimensional space. The positive aspects of these models consist in…

Given a particular prescription for the Einstein field equations (EFE's), it is important to have general protective theorems that lend support to it. The prescription of data on a timelike hypersurface for the (n + 1)-d EFE's arises in…