scispace - formally typeset
Journal ArticleDOI

Left-Degenerate Vacuum Metrics

Jerzy F. Plebański, +1 more
- 30 Aug 1976 - 
- Vol. 37, Iss: 9, pp 493-495
TLDR
For all complex space-times in which the self-dual part of the Weyl tensor is algebraically degenerate, Einstein's vacuum equations are reduced to a single differential equation of the second order and second degree as discussed by the authors.
Abstract: 
For all complex space-times in which the self-dual part of the Weyl tensor is algebraically degenerate, Einstein's vacuum equations are reduced to a single differential equation of the second order and second degree.

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Journal ArticleDOI

On the separation of Einsteinian substructures

Jerzy F. Plebański
- 01 Dec 1977 - 
TL;DR: Within the spinorial version of the Cartan structure formulas with the built-in (complex) Einstein vacuum equations some closed semi-Einsteinian substructures are isolated and discussed as discussed by the authors.
Journal ArticleDOI

The Theory of H-space

M. Ko, +3 more
- 01 May 1981 - 
TL;DR: The theory of H -space, the four-dimensional manifold of complex null hypersurfaces of an asymptotically flat space-time which are asymmptotic shear-free, is reviewed in this paper, and two independent formalisms for the derivation of the basic properties of H-space are presented.
Journal ArticleDOI

Killing vector fields in self-dual, Euclidean Einstein spaces with Λ¬=;0

M. Przanowski
- 01 Apr 1991 - 
TL;DR: In this paper, the authors considered self-dual, Euclidean Einstein spaces with nonvanishing cosmological term Λ and showed that in this case one can reduce ten Killing equations to one master equation.
Journal ArticleDOI

The intrinsic spinorial structure of hyperheavens

J. D. Finley, +1 more
- 01 Dec 1976 - 
TL;DR: In this paper, an inhomogeneous GL (2,C) group of coordinate transformations, constrained to leave the tetrad form invariant, is constructed and used to simplify the equations and clarify the geometrical meaning of the parameters introduced during the integration process.
Journal ArticleDOI

On the Einstein-Weyl and conformal self-duality equations

Maciej Dunajski, +2 more
- 03 Aug 2015 - 
TL;DR: The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as "master dispersionless systems" in four and three dimensions, respectively as mentioned in this paper.