Journal ArticleDOI
Recurrence conditions in space-time
TLDR
A general discussion of the recurrence properties of the Riemann, Ricci and Weyl tensors is given in this paper, where space-times possessing these properties are classified according to the Petrov type of the Ricci tensor and the Legre tensor.Abstract:
A general discussion of the recurrence properties of the Riemann, Ricci and Weyl tensors is given Space-times possessing these properties are classified according to the Petrov type of the Weyl tensor and the Legre type of the Ricci tensor The proofs of some known theorems are shortened and some new results are givenread more
Citations
More filters
Journal ArticleDOI
Homothetic transformations with fixed points in spacetime
TL;DR: A general discussion of homothetic motions in Einstein's theory is given in this paper, where general properties of such spacetimes are established, and a characterization of generalized plane wave spacetime is proved.
Journal ArticleDOI
Curvature structure in general relativity
Graham Hall,W. Kay +1 more
TL;DR: In this article, it was shown that the curvature and its first and second covariant derivatives essentially determine the metric stucture up to coordinate transformations, with the exception of generalized pp waves.
Journal ArticleDOI
Second-order symmetric Lorentzian manifolds: I. Characterization and general results
TL;DR: The n-dimensional Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor are characterized and classified in this paper, and the main result is that either they are locally symmetric or they have a covariantly constant null vector field, in this case defining a subfamily of Brinkmann's class in n dimensions.
Journal ArticleDOI
Recurrent conformal 2-forms on pseudo-Riemannian manifolds
TL;DR: In this paper, the notion of recurrent conformal 2-forms on a pseudo-Riemannian manifold of arbitrary signature was introduced, and it was shown that the Ricci tensor is Riemann compatible or equivalently, Weyl compatible.
Journal ArticleDOI
Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves
TL;DR: In this article, a complete classification of pseudo-Z symmetric space-times with harmonic conformal curvature tensors is presented, and a complete algebraic classification for the Weyl tensor is provided for n = 4.
References
More filters
Journal ArticleDOI
Gravitation: An Introduction to Current Research
Louis Witten,Jacques E. Romain +1 more
Journal ArticleDOI
Gravitational Waves in General Relativity. VI. The Outgoing Radiation Condition
TL;DR: In this paper, a covariant formulation of the outgoing radiation condition for gravitational fields is proposed, based on a detailed examination of the geometry of null lines and of the algebraic and differential properties of the Riemann tensor.
Journal ArticleDOI
The gravitational compass
TL;DR: In this paper, a purely covariant approach to general relativity, using the equation of geodesic deviation, is adopted, which is essentially that due to Pirani, but instead of using clouds of particles to analyze the gravitational field, a ''gravitational compass'' is proposed which fulfills the same purpose.
Related Papers (5)
Invariant two-spaces and canonical forms for the Ricci tensor in general relativity
W J Cormack,G S Hall +1 more