Gauge-Dependent Cosmological "Constant"

When the cosmological constant of spacetime is derived from the 5D induced-matter theory of gravity, we show that a simple gauge transformation changes it to a variable measure of the vacuum which is infinite at the big bang and decays to an astrophysically-acceptable value at late epochs. We outline implications of this for cosmology and galaxy formation.Comment: 14 pages, no figures, expanded version to be published in Class. Quantum Gra

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

Extra symmetry in the field equations in 5D with spatial spherical symmetry

We point out that the field equations in 5D, with spatial spherical symmetry, possess an extra symmetry that leaves them invariant. This symmetry corresponds to certain simultaneous interchange of coordinates and metric coefficients. As a consequence a single solution in 5D can generate very different scenarios in 4D, ranging from static configurations to cosmological situations. A new perspective emanates from our work. Namely, that different astrophysical and cosmological scenarios in 4D might correspond to the same physics in 5D. We present explicit examples that illustrate this point of view.Comment: Typos corrected. Accepted for publication in Classical and Quantum Gravit

Possible Wormhole Solutions in (4+1) Gravity

We extend previous analyses of soliton solutions in (4+1) gravity to new ranges of their defining parameters. The geometry, as studied using invariants, has the topology of wormholes found in (3+1) gravity. In the induced-matter picture, the fluid does not satisfy the strong energy conditions, but its gravitational mass is positive. We infer the possible existance of (4+1) wormholes which, compared to their (3+1) counterparts, are less exotic.Comment: 3 pages, latex, 1 figure

The Structure of the Big Bang from Higher-Dimensional Embeddings

We give relations for the embedding of spatially-flat Friedmann-Robertson-Walker cosmological models of Einstein's theory in flat manifolds of the type used in Kaluza-Klein theory. We present embedding diagrams that depict different 4D universes as hypersurfaces in a higher dimensional flat manifold. The morphology of the hypersurfaces is found to depend on the equation of state of the matter. The hypersurfaces possess a line-like curvature singularity infinitesimally close to the $t = 0^+$ 3-surface, where $t$ is the time expired since the big bang. The family of timelike comoving geodesics on any given hypersurface is found to have a caustic on the singular line, which we conclude is the 5D position of the point-like big bang.Comment: 11 pages, 5 figures, revtex4, accepted in Class. Quant. Gra

Null Geodesics in Five Dimensional Manifolds

We analyze a class of 5D non-compact warped-product spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the so-called canonical coordinate gauge of Mashhoon et al. We confirm that if the 5D manifold in our model is Ricci-flat, then there is an induced cosmological constant in the 4D sub-manifold. We derive the general form of the 5D Killing vectors and relate them to the 4D Killing vectors of the embedded spacetime. We then study the 5D null geodesic paths and show that the 4D part of the motion can be timelike -- that is, massless particles in 5D can be massive in 4D. We find that if the null trajectories are affinely parameterized in 5D, then the particle is subject to an anomalous acceleration or fifth force. However, this force may be removed by reparameterization, which brings the correct definition of the proper time into question. Physical properties of the geodesics -- such as rest mass variations induced by a variable cosmological ``constant'', constants of the motion and 5D time-dilation effects -- are discussed and are shown to be open to experimental or observational investigation.Comment: 19 pages, REVTeX, in press in Gen. Rel. Gra

Induced Matter and Particle Motion in Non-Compact Kaluza-Klein Gravity

We examine generalizations of the five-dimensional canonical metric by including a dependence of the extra coordinate in the four-dimensional metric. We discuss a more appropriate way to interpret the four-dimensional energy-momentum tensor induced from the five-dimensional space-time and show it can lead to quite different physical situations depending on the interpretation chosen. Furthermore, we show that the assumption of five-dimensional null trajectories in Kaluza-Klein gravity can correspond to either four-dimensional massive or null trajectories when the path parameterization is chosen properly. Retaining the extra-coordinate dependence in the metric, we show the possibility of a cosmological variation in the rest masses of particles and a consequent departure from four-dimensional geodesic motion by a geometric force. In the examples given, we show that at late times it is possible for particles traveling along 5D null geodesics to be in a frame consistent with the induced matter scenario.Comment: 29 pages, accepted to GR

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