  Finsler geometry is a natural and fundamental generalization of Riemann
geometry. The Finsler structure depends on both coordinates and velocities. It
is defined as a function on tangent bundle of a manifold. We use the Bianchi
identities satisfied by Chern curvature to set up a gravitation theory in
Berwald-Finsler space. The geometric part of the gravitational field equation
is nonsymmetric in general. This indicates that the local Lorentz invariance is
violated. Nontrivial solutions of the gravitational field equation are
presented.
