Ideally embedded space-times

Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.Comment: layout changed and typos corrected; uses revtex

The embedding of the spacetime in five-dimensional spaces with arbitrary non-degenerate Ricci tensor

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 the Ricci tensor of an arbitrary specified space. This may be regarded as a further extension of the Campbell-Magaard theorem. We highlight the significance of embedding theorems of increasing degrees of generality in the context of higher dimensional spacetimes theories and illustrate the new theorem by establishing the embedding of a general class of Ricci-flat spacetimes

On the embedding of branes in five-dimensional spaces

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 brane. We then consider the embedding in the context of Randall-Sundrum-type models, taking into account $Z_{2}$ symmetry and a cosmological constant. We employ the Campbell-Magaard theorem to construct the embeddings and are led to the conclusion that the content of energy-matter of the brane does not necessarily determine its curvature. Finally, as an application to illustrate our results, we construct the embedding of Minkowski spacetime filled with dust.Comment: 12 pages - REVTEX To appear in Classical and Quantum Gravit

Embeddings in Spacetimes Sourced by Scalar Fields

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 found, and to Brans-Dicke theory. The relationship between Campbell-Magaard theorem and the general relativity, Cauchy and initial value problems is outlined.Comment: RevTEX (11 pages)/ To appear in the Journal of Mathematical Physic

Naturally occurring C-terminal splice variants of nuclear receptors

Alternative mRNA splicing in the region encoding the C-terminus of nuclear receptors results in receptor variants lacking the entire ligand-binding domain (LBD), or a part of it, and instead contain a sequence of splice variant-specific C-terminal amino acids. A total of thirteen such splice variants have been shown to occur in vertebrates, and at least nine occur in humans. None of these receptor variants appear to be able to bind endogenous ligands and to induce transcription on promoters containing the response element for the respective canonical receptor variant. Interestingly, ten of these C-terminal splice variants have been shown to display dominant-negative activity on the transactivational properties of their canonical equivalent. Research on most of these splice variants has been limited, and the dominant-negative effect of these receptor variants has only been demonstrated in reporter assays in vitro, using transiently transfected receptors and reporter constructs. Therefore, the in vivo function and relevance of most C-terminal splice variants remains unclear. By reviewing the literature on the human glucocorticoid receptor β-isoform (hGRβ), we show that the dominant-negative effect of hGRβ is well established using more physiologically relevant readouts. The hGR β-isoform may alter gene transcription independent from the canonical receptor and increased hGRβ levels correlate with glucocorticoid resistance and the occurrence of several immune-related diseases. Thus, available data suggests that C-terminal splice variants of nuclear receptors act as dominant-negative inhibitors of receptor-mediated signaling in vivo, and that aberrant expression of these isoforms may be involved in the pathogenesis of a variety of diseases

Dynamically generated embeddings of spacetime

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 evolution of initial data given in a four-dimensional spacelike hypersurface. By using the CM theorem, we establish that for any analytic spacetime, there exist appropriate initial data whose Cauchy development is a five-dimensional vacuum space into which the spacetime is locally embedded. We shall see also that the spacetime embedded is Cauchy stable with respect these the initial data.Comment: (8 pages, 1 figure). A section on Cauchy Stability of the embedding was added. (To appear in Class. Quant. Grav.

Wave-like Solutions for Bianchi type-I cosmologies in 5D

We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and "wave-like". In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type-I, which can be applied to our universe after the big-bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry