Journal ArticleDOI
Riemannian Curvature and the Petrov Classification
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In this paper, a connection between the Riemannian Curvatures of the wave surfaces of a null vector I at a point p in space-time and the Petrov type of the space time at p is shown.Abstract:
A connection is shown between the Riemannian Curvatures of the wave surfaces of a null vector I at a point p in space-time and the Petrov type of the space-time at p. Some other results on Riemannian Curvature are discussedread more
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The classification of the Ricci and Plebański tensors in general relativity using Newman–Penrose formalism
TL;DR: In this paper, a list of a canonical set of the Newman-Penrose quantities ΦAB, the tetrad components of the trace-free Ricci tensor, for each Plebanski class according to the classification of this tensor is given.
Journal ArticleDOI
Complex relativity and real solutions II: Classification of complex bivectors and metric classes
TL;DR: In this paper, a generalization of the Mariot-Robinson theorem from real relativity is given and related to various canonical forms of complex bivectors, and four classes of real metrics of the first class are ones with a null congruence whose wave surfaces have equal curvature.
Journal ArticleDOI
Sectional curvature and tidal accelerations
John K. Beem,Phillip E. Parker +1 more
TL;DR: For Ricci flat four-dimensional space-times, repeated principal null directions were characterized as repeated principal nonsmooth null directions in this paper, which is a characterization of null directions that fail to satisfy the generic condition used in singularity theorems.
Journal ArticleDOI
Null hypersurfaces in Lorentzian manifolds II
TL;DR: In this paper, the geometrical properties of null hypersurfaces in Lorentzian manifolds are studied and the authors consider the problem of normalizing a null vector lying in the tangent plane.
Journal ArticleDOI
Riemannian curvature and the classification of the Riemann and Ricci tensors in space-time
W. J. Cormack,Graham Hall +1 more
TL;DR: In this article, the connection between the critical point structure of the Riemannian curvature function and the Petrov classification of the Ricci tensor has been investigated, and a similar function is defined whose critical point structures are connected with the algebraic classification of RicCI tensors.
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