Orthogonal separation of variables for the Hamilton-Jacobi and wave equations in three-dimensional Minkowski space

Abstract

We give a complete solution of the Eisenhart integrability conditions in three-dimensional Minkowski space obtaining 39 orthogonally separable webs and 58 inequivalent metrics in adapted coordinate systems which permit orthogonal separation of variables for the associated Hamilton-Jacobi and wave equations. The corresponding transformations from canonical separable coordinates to canonical pseudo-Cartesian coordinates are listed for each of the 58 cases and characteristic Killing tensors are given for each of the 39 webs.