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arXiv · 1802.01537

The Bach equations in Spin-Coefficient form

Hamish Forbes
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Abstract

Conformal gravity theories are defined by field equations that determine only the conformal structure of the spacetime manifold. The Bach equations represent an early example of such a theory, we present them here in component form in terms of spin- and boost-weighted spin-coefficients using the compacted spin-coefficient formalism. These equations can be used as an efficient alternative to the standard tensor form. As a simple application we solve the Bach equations for pp-wave and static spherically symmetric spacetimes.

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Hamish Forbes. 2018-02-05. The Bach equations in Spin-Coefficient form. https://doi.org/10.1088/1361-6382%2Faac1eb

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