Identifying Berwald Finsler geometries

Berwald geometries are Finsler close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which given Lagrangian has satisfy be of type. Applied $(\alpha,\beta)$-Finsler spaces, respectively $(A,B)$-Finsler spacetimes, this reduces condition for the Levi-Civita covariant derivative defining $1$-form. illustrate our results with novel examples $(\alpha,\beta)$-Berwald represent Finslerian versions Kundt (constant scalar invariant) spacetimes. The generalize earlier findings by Tavakol van den Bergh, well conditions Randers m-Kropina resp. very special/general relativity