Journal ArticleDOI
Spaces Conformal to a Class of Spaces in General Relativity
TLDR
In this paper, a study of conformal transformations of a Riemannian V$_4$ is made within the framework of the Penrose spinor formalism, and necessary and sufficient conditions are established for a space to be conformal to a space in which the conform tensor is divergence-free.Abstract:
A study of conformal transformations of a Riemannian V$_4$ is made within the framework of the Penrose spinor formalism. In particular the conformal properties of a whole hierarchy of spaces occurring in general relativity are considered, and necessary and sufficient conditions are established for a space to be conformal (a) to a space in which the conform tensor is divergence-free, (b) to an empty space, (c) to an Einstein space. The case of Petrov type N has to be treated separately.read more
Citations
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Obstructions to conformally Einstein metrics in n dimensions
A. Rod Gover,Pawel Nurowski +1 more
TL;DR: It is shown that there is an alternative characterisation of conformally Einstein metrics based on the tractor connection associated with the normal conformal Cartan bundle, which plays a key role in constructing some of the invariants.
Journal ArticleDOI
Conformal Einstein spaces
TL;DR: In this paper, a new set of necessary and sufficient conditions for a space to be conformal to an Einstein space is presented, and the vanishing of the Bach tensor is used to define the class of spaces conformally related to C spaces.
Journal ArticleDOI
New conformal gauging and the electromagnetic theory of Weyl
TL;DR: In this article, the Maurer-Cartan structure equations were derived and the zero curvature solutions for the conformal connection were found for general curved eight-dimensional geometries to be in 1-1 correspondence with four-dimensional Einstein-Maxwell space.
Journal ArticleDOI
Anti-self-dual Conformal Structures with Null Killing Vectors from Projective Structures
Maciej Dunajski,S. West +1 more
TL;DR: In this article, the twistor space of a real analytic neutral signature anti-self-dual conformal structure (M, [g]) with a null conformal Killing vector is constructed.
Journal ArticleDOI
Weyl geometry
TL;DR: Weyl curvature tensors are invariant to the Riemann curvature as mentioned in this paper, which is the conformally invariant part of the Weyl tensor tensor, and the Ricci and Schouten tensors required to insure conformal invariance.
References
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Journal ArticleDOI
A spinor approach to general relativity
TL;DR: In this article, a calculus for general relativity is developed in which the basic role of tensors is taken over by spinors, and the Riemann-Christoffel tensor is written in a spinor form according to a scheme of Witten.