An exact solution of the five-dimensional Einstein equations with four-dimensional de Sitter-like expansion

We present an exact solution to the Einstein field equations which is Ricci and Riemann flat in five dimensions, but in four dimensions is a good model for the early vacuum-dominated universe.Comment: 6 pages; to appear in Journal of Mathematical Physics; v2: reference 3 correcte

FLRW Universes from "Wave-Like" Cosmologies in 5D

We consider the evolution of a 4D-universe embedded in a five-dimensional (bulk) world with a large extra dimension and a cosmological constant. The cosmology in 5D possesses "wave-like" character in the sense that the metric coefficients in the bulk are functions of the extra coordinate and time in a way similar to a pulse or traveling wave propagating along the fifth dimension. This assumption is motivated by some recent work presenting the big-bang as a higher dimensional shock wave. We show that this assumption, together with an equation of state for the effective matter quantities in 4D, allows Einstein's equations to be fully integrated. We then recover the familiar FLRW universes, on the four-dimensional hypersurfaces orthogonal to the extra dimension. Regarding the extra dimension we find that it is {\em growing} in size if the universe is speeding up its expansion. We also get an estimate for the relative change of the extra dimension over time. This estimate could have important observational implications, notably for the time variation of rest mass, electric charge and the gravitational "constant". Our results extend previous ones in the literature.Comment: Few comments added, references updated. To appear in Int. J. of Mod. Phys.

Stabilization of test particles in Induced Matter Kaluza-Klein theory

The stability conditions for the motion of classical test particles in an $n$-dimensional Induced Matter Kaluza-Klein theory is studied. We show that stabilization requires a variance of the strong energy condition for the induced matter to hold and that it is related to the hierarchy problem. Stabilization of test particles in a FRW universe is also discussed.Comment: 15 pages, 1 figure, to appear in Class. Quantum Gra

Upper limit to ΩB\Omega_B in scalar-tensor gravity theories

In a previous paper (Serna & Alimi 1996), we have pointed out the existence of some particular scalar-tensor gravity theories able to relax the nucleosynthesis constraint on the cosmic baryonic density. In this paper, we present an exhaustive study of primordial nucleosynthesis in the framework of such theories taking into account the currently adopted observational constraints. We show that a wide class of them allows for a baryonic density very close to that needed for the universe closure. This class of theories converges soon enough towards General Relativity and, hence, is compatible with all solar-system and binary pulsar gravitational tests. In other words, we show that primordial nucleosynthesis does not always impose a very stringent bound on the baryon contribution to the density parameter.Comment: uuencoded tar-file containing 16 pages, latex with 5 figures, accepted for publication in Astrophysical Journal (Part 1

Causal Anomalies in Kaluza-Klein Gravity Theories

Causal anomalies in two Kaluza-Klein gravity theories are examined, particularly as to whether these theories permit solutions in which the causality principle is violated. It is found that similarly to general relativity the field equations of the space-time-mass Kaluza-Klein (STM-KK) gravity theory do not exclude violation of causality of G\"odel type, whereas the induced matter Kaluza-Klein (IM-KK) gravity rules out noncausal G\"odel-type models. The induced matter version of general relativity is shown to be an efficient therapy for causal anomalies that occurs in a wide class of noncausal geometries. Perfect fluid and dust G\"odel-type solutions of the STM-KK field equations are studied. It is shown that every G\"odel-type perfect fluid solution is isometric to the unique dust solution of the STM-KK field equations. The question as to whether 5-D G\"odel-type non-causal geometries induce any physically acceptable 4-D energy-momentum tensor is also addressed.Comment: 16 page. LaTex file. To appear in Int. J. Mod. Phys. A (1998

An exact self-similar solution for an expanding ball of radiation

We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The matter satisfies the usual energy and thermodynamic conditions. The energy density and temperature are related by the Stefan-Boltzmann law. The solution admits a homothetic Killing vector in $5D$, which induces the existence of self-similar symmetry in 4D, where the line element as well as the dimensionless matter quantities are invariant under a simple "scaling" group.Comment: New version expanded and improved. To appear in Int. J. Mod. Phys.

Wesson's IMT with a Weylian bulk

The foundations of Wesson's induced matter theory are analyzed. It is shown that the 5D empty bulk must be regarded rather as a Weylian space than as a Riemannian one.The framework of a Weyl-Dirac version of Wesson's theory is elaborated and discussed. The bulk possesses in addition to the metric tensor a Weylian connection vector as well Dirac's gauge function; there are no sources (mass, current) in the bulk. On the 4D brane one obtains a geometrically based unified theory of gravitation and electromagnetism with mass, currents and equations induced by the 5D bulkComment: 29 page

Static Ricci-flat 5-manifolds admitting the 2-sphere

We examine, in a purely geometrical way, static Ricci-flat 5-manifolds admitting the 2-sphere and an additional hypersurface-orthogonal Killing vector. These are widely studied in the literature, from different physical approaches, and known variously as the Kramer - Gross - Perry - Davidson - Owen solutions. The 2-fold infinity of cases that result are studied by way of new coordinates (which are in most cases global) and the cases likely to be of interest in any physical approach are distinguished on the basis of the nakedness and geometrical mass of their associated singularities. It is argued that the entire class of solutions has to be considered unstable about the exceptional solutions: the black string and soliton cases. Any physical theory which admits the non-exceptional solutions as the external vacuua of a collapsing object has to accept the possibility of collapse to zero volume leaving behind the weakest possible, albeit naked, geometrical singularities at the origin.Finally, it is pointed out that these types of solutions generalize, in a straightforward way, to higher dimensions.Comment: Generalize, in a straightforward way, to higher dimension

Universal features of dimensional reduction schemes from general covariance breaking

Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors, that successfully generalize to one side Kaluza–Klein gauge fields and to the other side extrinsic curvature and torsion of embedded spaces, thus fully characterizing the geometry of dimensional reduction. We obtain general formulas for the reduction of the main tensors and operators of Riemannian geometry. In particular, we provide what is probably the maximal possible generalization of Gauss, Codazzi and Ricci equations and various other standard formulas in Kaluza–Klein and embedded spacetimes theories. After general covariance breaking, part of the residual covariance is perceived by effective lower dimensional observers as an infinite dimensional gauge group. This reduces to finite dimensions in Kaluza–Klein and other few remarkable backgrounds, all characterized by the vanishing of appropriate lower dimensional tensors

On the Axiomatics of the 5-dimensional Projective Unified Field Theory of Schmutzer

For more than 40 years E.Schmutzer has developed a new approach to the (5-dimensional) projective relativistic theory which he later called Projective Unified Field Theory (PUFT). In the present paper we introduce a new axiomatics for Schmutzer's theory. By means of this axiomatics we can give a new geometrical interpretation of the physical concept of the PUFT.Comment: 32 pages, 1 figure, LaTeX 2e, will be submitted to Genaral Relativity and Gravitatio