Determining the number of Killing tensors by (linear) algebra

Abstract

It is a natural problem to determine the number of independent Killing tensors of a certain rank that a given metric admits. In this paper, it is discussed how this problem can be addressed in a computer-algebraic way. Pseudo-Riemannian metrics expressed in local coordinates are considered, with and without parameter dependence. No assumption is made about analyticity of the Killing tensors.