Note on Finslerian relativity

Abstract

Finslerian structure of spacetime is investigated. For a special type of generalized Finsler metric the explicit expression of Cartan-like metrical connection is derived and it is shown that it resembles the usual one. Causal problems in Finsler-type spacetime are discussed and, based on the arguments, the Einstein-type equations for the Finslerian quantities are derived by using the lifting of a Finsler metric to a tangent bundle. It is shown that a solution of the proposed equations can also be obtained from the complex structure of the tangent bundle. One-form type metrics are used to discuss the geometrical interpretation of isosymmetry. A simple way of obtaining a metrical connection for a general generalized Finsler metric is given.