Killing Invariants and the Subclassification Problem

The Cartan-Karlhede (CK) algorithm is a method of determining if two metrics are equivalent implying that one metric can be transformed into the other via a coordinate transformation. While this method is very powerful, the Cartan curvature invariants produced from each metric in the algorithm are often too complicated to compare. Furthermore, finding a solution to the equations by equating the invariants from each metric may be undecidable. In this work, we outline a proposed method to define a new set of differential invariants derived from Killing vector fields that we hope will provide a simpler method of comparing spacetimes. As examples, we apply this method first to static spherically symmetric metrics and then to the class of stationary axisymmetric metrics both of Boyer-Lindquist and non-Boyer-Lindquist form to demonstrate the utility of Killing Invariants to distinguish different spacetimes.