On the limits of Brans-Dicke spacetimes: a coordinate-free approach

We investigate the limit of Brans-Dicke spacetimes as the scalar field coupling constant omega tends to infinity applying a coordinate-free technique. We obtain the limits of some known exact solutions. It is shown that these limits may not correspond to similar solutions in the general relativity theory.Comment: LaTeX, 16 pp, report DF/UFPB/02-9

Equivalence of three-dimensional spacetimes

A solution to the equivalence problem in three-dimensional gravity is given and a practically useful method to obtain a coordinate invariant description of local geometry is presented. The method is a nontrivial adaptation of Karlhede invariant classification of spacetimes of general relativity. The local geometry is completely determined by the curvature tensor and a finite number of its covariant derivatives in a frame where the components of the metric are constants. The results are presented in the framework of real two-component spinors in three-dimensional spacetimes, where the algebraic classifications of the Ricci and Cotton-York spinors are given and their isotropy groups and canonical forms are determined. As an application we discuss Goedel-type spacetimes in three-dimensional General Relativity. The conditions for local space and time homogeneity are derived and the equivalence of three-dimensional Goedel-type spacetimes is studied and the results are compared with previous works on four-dimensional Goedel-type spacetimes.Comment: 13 pages - content changes and corrected typo

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.Comment: 19 p

Riemann-Cartan Space-times of G\"odel Type

A class of Riemann-Cartan G\"odel-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 G\"odel-type space-times. The equivalence of Riemann-Cartan G\"odel-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 $\ell, m^2, \omega$: identical triads ($\ell, m^2, \omega$) correspond to locally equivalent manifolds. The algebraic types of the irreducible parts of the curvature and torsion tensors are also presented.Comment: 24 pages, LaTeX fil

Limits of space-times in five dimensions and their relation to the Segre Types

A limiting diagram for the Segre classification in 5-dimensional space-times is obtained, extending a recent work on limits of the energy-momentum tensor in general relativity. Some of Geroch's results on limits of space-times in general relativity are also extended to the context of five-dimensional Kaluza-Klein space-times.Comment: Late

The Levi-Civita spacetime

We consider two exact solutions of Einstein's field equations corresponding to a cylinder of dust with net zero angular momentum. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust particles is constant [1]. For both solutions we studied the junction conditions to the exterior static vacuum Levi-Civita spacetime. From this study we find an upper limit for the energy density per unit length $\sigma$ of the source equal ${1\over 2}$ for the first case and ${1\over 4}$ for the second one. Thus the homogeneous cluster provides another example [2] where the range of $\sigma$ is extended beyond the limit value ${1\over 4}$ previously found in the literature [3,4]. Using the Cartan Scalars technics we show that the Levi-Civita spacetime gets an extra symmetry for $\sigma={1\over 2}$ or ${1\over 4}$. We also find that the cluster of homogeneous dust has a superior limit for its radius, depending on the constant volumetric energy density $\rho_0$

Segre Types of Symmetric Two-tensors in n-Dimensional Spacetimes

Three propositions about Jordan matrices are proved and applied to algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type spacetimes. We show that the possible Segre types are [1,1...1], [21...1], [31\ldots 1], [z\bar{z}1...1] and degeneracies thereof. A set of canonical forms for the Segre types is obtained in terms of semi-null bases of vectors.Comment: 14 pages, LaTeX, replaced due to a LaTex erro