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On the compatibility of Lorentz-metrics with linear connections on 4-dimensional manifolds

G. S. Hall·D. P. Lonie
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Abstract

This paper considers 4-dimensional manifolds upon which there is a Lorentz metric, h, and a symmetric connection and which are originally assumed unrelated. It then derives sufficient conditions on the metric and connection (expressed through the curvature tensor) for the connection to be the Levi-Civita connection of some (local) Lorentz metric, g, and calculates the relationship between g and h. Some examples are provided which help to assess the strength of the sufficient conditions derived.

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G. S. Hall, D. P. Lonie. 2005-09-16. On the compatibility of Lorentz-metrics with linear connections on 4-dimensional manifolds. https://doi.org/10.1088/0305-4470%2F39%2F12%2F009

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