For torsion-free connections with vectorial nonmetricity, necessary and sufficient conditions are derived for Finsler metrizability, with explicit Lagrangian construction when the conditions hold.
Weyl geometric gravity black holes in light of the solar system tests.The European Physical Journal C, 85(11):1325
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On the Finsler variational nature of autoparallels in metric-affine geometry
For torsion-free connections with vectorial nonmetricity, necessary and sufficient conditions are derived for Finsler metrizability, with explicit Lagrangian construction when the conditions hold.