Classification of second order symmetric tensors in five-dimensional Kaluza–Klein-type theories

Abstract

An algebraic classification of second order symmetric tensors in five-dimensional Kaluza–Klein-type Lorentzian spaces is presented by using Jordan matrices. It is shown that the possible Segre types are [1,1111], [2111], [311], [zz̄111], and the degeneracies thereof. A set of canonical forms for each Segre type is found. The possible continuous groups of symmetry for each canonical form are also studied.