arXiv subjects

M. A. H. MacCallum

Publications and source records attributed to M. A. H. MacCallum.

25 records · Page 2Linked to original sources

arXiv1997

Stationary and static cylindrically symmetric Einstein spaces of the Lewis form

The derivation of the general solutions for stationary and static cylindrically symmetric Einstein spaces of Lewis form is revisited and the physical and geometrical meaning of the parameters appearing in the resulting solutions are investigated. It is shown that three of the parameters (and the value of the cosmological constant) are essential, of which one characterizes the local gravitational field and appears in the Cartan scalars, while the remaining two give information about the topological identification made to produce cylindrical symmetry. Other than the cosmological constant, they can be related to the parameters of the vacuum Weyl and Lewis classes, whose interpretation was previously investigated by da Silva et al. (1995a, 1995b).

gr-qc↗

arXiv1997

Riemann-Cartan Space-times of Gödel Type

A class of Riemann-Cartan Gödel-type space-times are examined in the light of the equivalence problem techniques. The conditions for local space-time homogeneity are derived, generalizing previous works on Riemannian Gödel-type space-times. The equivalence of Riemann-Cartan Gödel-type space-times of this class is studied. It is shown that they admit a five-dimensional group of affine-isometries and are characterized by three essential parameters $\ell, m^2, ω$: identical triads ($\ell, m^2, ω$) correspond to locally equivalent manifolds. The algebraic types of the irreducible parts of the curvature and torsion tensors are also presented.

gr-qc↗

arXiv1997

An exterior for the Gödel spacetime

We match the vacuum, stationary, cylindrically symmetric solution of Einstein's field equations with $Λ$, in a form recently given by Santos, as an exterior to an infinite cylinder of dust cut out of a Gödel universe. There are three cases, depending on the radius of the cylinder. Closed timelike curves are present in the exteriors of some of the solutions. There is a considerable similarity between the spacetimes investigated here and those of van Stockum referring to an infinite cylinder of rotating dust matched to vacuum, with $Λ=0$.

gr-qc↗

arXiv1997

Hypersurface-orthogonal generators of an orthogonally transitive transitive $G_2I$, topological identifications, and axially and cylindrically symmetric spacetimes

A criterion given by Castejon-Amenedo and MacCallum (1990) for the existence of (locally) hypersurface-orthogonal generators of an orthogonally-transitive two-parameter Abelian group of motions (a $G_2I$) in spacetime is re-expressed as a test for linear dependence with constant coefficients between the three components of the metric in the orbits in canonical coordinates. In general, it is shown that such a relation implies that the metric is locally diagonalizable in canonical coordinates, or has a null Killing vector, or can locally be written in a generalized form of the `windmill' solutions characterized by McIntosh. If the orbits of the $G_2I$ have cylindrical or toroidal topology and a periodic coordinate is used, these metric forms cannot in general be realized globally as they would conflict with the topological identification. The geometry then has additional essential parameters, which specify the topological identification. The physical significance of these parameters is shown by their appearance in global holonomy and by examples of exterior solutions where they have been related to characteristics of physical sources. These results lead to some remarks about the definition of cylindrical symmetry.

gr-qc↗

arXiv1993

On limits of spacetimes -- a coordinate-free approach

A coordinate-free approach to limits of spacetimes is developed. The limits of the Schwarzschild metric as the mass parameter tends to 0 or $\infty$ are studied, extending previous results. Besides the known Petrov type D and 0 limits, three vacuum plane-wave solutions of Petrov type N are found to be limits of the Schwarzschild spacetime.

gr-qc↗

arXiv1992

Inhomogeneous and anisotropic cosmologies

This is a review of cosmological models prepared for the Pont d'Oye workshop on the origin of structure in the universe. The classes of models are discussed in turn, and then some of their uses are considered.

gr-qc↗

arXiv1992

Anisotropic and inhomogeneous cosmologies

This review was given at the 65th birthday meeting of D.W. Sciama, The Renaissance of General Relativity and Cosmology, to be published by Cambridge University Press. It presents progress in the understanding of non-standard relativistic cosmologies during Sciama's career, organized by the areas of application rather than the mathematical types of the models.

gr-qc↗