New class of Finsler metrics (Q1263093)

The author considers a new class of Finsler metrics \(F(x,y) = [(\eta_{\alpha\beta} + kB_{\alpha} B_{\beta}) y^{\alpha} y^{\beta}]^{1/2}\), where \(B_{\alpha} = B_{\alpha}(x,y)\), \(k\) is a constant and \(\eta_{\alpha\beta}\) is of signature \((+1,-1,-1,-1)\). Various properties of these metrics are proved. Six particular choices of \(B_\alpha\) of physical interest are pointed out. It is shown that one of them produces a geodesic equation which is equivalent to the Lorentz equation of motion for a charged particle.