On the compatibility of Lorentz metrics with linear connections on 4-dimensional manifolds
نویسندگان
چکیده
This paper considers 4-dimensional manifolds upon which there is a Lorentz metric h and a symmetric connection Γ and which are originally assumed unrelated. It then derives sufficient conditions on h and Γ (expressed through the curvature tensor of Γ) for Γ 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. Submitted to: Class. Quantum Grav. PACS numbers: 04.20.-q, 04.20.Cv, 02.40.Ky On the compatibility of Lorentz metrics with linear connections 2
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