Des J. McManus

Five‐dimensional cosmological models in induced matter theory

A class of five‐dimensional space–times that contain four‐dimensional hypersurfaces whose intrinsic metrics are Friedman–Robertson–Walker (FRW) metrics is examined (the four‐dimensional intrinsic Lorentzian metrics are both spatially homogeneous and isotropic). The five‐dimensional vacuum field equations, 5Gij=0, are shown to induce four‐dimensional perfect‐fluid FRW field equations, 4Gij=4Tij, and thus these FRW cosmological models may be interpreted as being purely geometrical in origin.

A family of cosmological solutions in higher‐dimensional Einstein gravity

A two‐parameter family of solutions to Einstein’s vacuum field equations in six dimensions is presented. The solutions are a natural extension of a one‐parameter family of five‐dimensional vacuum solutions found by Ponce de Leon [Gen. Relativ. Gravit. 20, 539 (1988)] and are closely related to the generalized Kasner metrics. The solution is generalized to 4+n dimensions and is briefly discussed.

Shear-free, irrotational, geodesic, anisotropic fluid cosmologies

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a co-moving observer, satisfy an equation of state of the form , with , then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.

Spherically Symmetric Solutions of Einstein's Vacuum Equations in Five Dimensions

Multi-dimensional spherically symmetric spacetimes are of interest in the study of higher-dimensional black holes (and solitons) and higher-dimensional cosmological models. In this paper we shall present a comprehensive investigation of solutions of the five-dimensional spherically symmetric vacuum Einstein field equations subject only to the condition of separability in the radial coordinate (but not necessarily in the remaining two coordinates). A variety of new solutions are found which generalize a number of previous results. The properties of these solutions are discussed with particular attention being paid to their possible astrophysical and cosmological applications. In addition, the four-dimensional properties of matter can be regarded as geometrical in origin by a reduction of the five-dimensional vacuum field equations to Einsteins four-dimensional theory with a non-zero energy-momentum tensor constituting the material source; we shall also be interested in the induced matter associated with the new five-dimensional solutions obtained.

Riemannian three‐metrics with degenerate Ricci tensors

A complete classification of Riemannian three‐metrics whose Ricci tensor possesses exactly two distinct constant eigenvalues is given: those metrics that admit a G4 as the maximal isometry group belong to either Petrov case IIIq=0, or VII, or VIII; those metrics that admit a G3 as the maximal isometry group belong to either Bianchi class VI0, or VIII, or IX. An explicit coordinate representation is given for all the homogeneous and inhomogeneous solutions.

Lorentzian three‐metrics with degenerate Ricci tensors

A classification of Lorentzian three‐metrics whose Ricci tensor satisfies Rij=λ1gij+λ2vivj with λ1 and λ2(≠0) constant where vivi=κ(=0 or ±1) is given. An explicit coordinate representation is given for all the metrics that admit a G4 group as their maximal isometry group. Those metrics that admit a G3 as their maximal isometry group belong to either Bianchi class VI0, or VII0, or VIII, or IX when κ ≠ 0, and to either Bianchi class III, or IV, or VI0, VIh, or VIII when κ=0. An explicit coordinate representation is given for all the inhomogeneous solutions in the case κ ≠ 0.