Related papers: The Friedmann-Lemaitre models in perspective
Equations for submanifolds, which correspond to embeddings of the four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are presented in convenient form in general case. Several specific examples are considered.
We investigate a class of semi-Riemannian manifolds characterized by smooth metric signature changes with a transverse radical. This class includes spacetimes relevant to cosmological models such as the Hartle-Hawking "no boundary"…
In this paper, we have reintroduced a new approach to conformal geometry developed and presented in two previous papers, in which we show that all n-dimensional pseudo-Riemannian metrics are conformal to a flat n-dimensional manifold as…
In this paper we extend the Cartan's approach of Riemannian normal coordinates and show that all n-dimensional pseudo-Riemannian metrics are conformal to a flat manifold, when, in normal coordinates, they are well-behaved in the origin and…
A natural one codimension isometric embedding of each $(n+1)$-dimensional spherical Robertson-Walker (RW) spacetime $I\times_f \mathbb{S}^n$ in $(n+2)$-dimensional Lorentz-Minkowski spacetime $\mathbb{L}^{n+2}$ permits to contemplate…
We characterize those spacetimes which admit a isometric (or conformal) embedding in some Lorentz-Minkowski space L^N. In particular, any globally hyperbolic spacetime can be isometrically embedded in L^N. This is proven by a result of its…
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…
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…
Stated succinctly, the original version of the Campbell-Magaard theorem says that it is always possible to locally embed any solution of 4-dimensional general relativity in a 5-dimensional Ricci-flat manifold. We discuss the proof of this…
We describe embeddings of $n$-dimensional Lorentzian manifolds, including Friedmann-Lema\^itre-Robertson-Walker spaces, in $\mathbb{R}^{n+2}$ such that the metrics of the submanifolds are inherited by a restriction from that of…
Embedding theorems have continued to be a topic of interest in the general theory of relativity since these help connect the classical theory to higher-dimensional manifolds. This paper deals with spacetimes of embedding class one, i.e.,…
It is well-known that the Einstein condition on warpedgeometries requires the fibres to be necessarily Einstein. However, exact warped solutions have often been obtained using one- and two-dimensional bases. In this paper, keeping the…
Earlier Chicone, Latushkin and Montgomery-Smith [Comm Math Phys (1997)] have shown that a fast dynamo in compact two-dimensional manifold can be supported as long as its Riemannian curvature be negative. Recently Klebanov and Maldacena…
We give necessary and sufficient conditions for a semi-Riemannian manifold of arbitrary signature to be locally isometrically immersed into certain warped products. Then, we describe a way to use the structure equations of such immersions…
We study isometric embeddings of some solutions of the Einstein equations with suffciently high symmetries into a flat ambient space. We briefly describe a method for constructing surfaces with a given symmetry. We discuss all minimal…
We study trapped surfaces from the point of view of local isometric embedding into three-dimensional Riemannian manifolds. When a two-surface is embedded into three-dimensional Euclidean space, the problem of finding all surfaces applicable…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
The idea of an oscillating Universe has remained a topic of interest even after the discovery of dark energy. This paper confirms this idea by means of another well-established theory in general relativity, the embedding of curved…
The general formalism of the free Dirac fermions on spatially flat $(1+3)$-dimensional Friedmann-Lema\^ itre-Robertson-Walker (FLRW) spacetimes is developed in momentum representation. The mode expansions in terms of the fundamental spinors…
Let $M^{n}$ be an $n$-dimensional complete spacelike linear Weingarten submanifold immersed in a locally symmetric semi-Riemannian space $\mathbb{L}_{q}^{n+p}$ of index $q$, with parallel normalized mean curvature vector field and flat…