%0 Journal Article %T Killing Operator for the Kerr Metric %A J.-F. Pommaret %J Journal of Modern Physics %P 31-59 %@ 2153-120X %D 2023 %I Scientific Research Publishing %R 10.4236/jmp.2023.141003 %X When D: E → F is a linear differential operator of order q between the sections of vector bundles over a manifold X of dimension n, it is defined by a bundle map Φ: Jq(E) → F=F0 that may depend, explicitly or implicitly, on constant parameters a, b, c, ... . A ˇ°direct problemˇ± is to find the generating compatibility conditions (CC) in the form of an operator D1: F0 → F1. When D is involutive, that is when the corresponding system Rq = ker (Φ) is involutive, this procedure provides successive first order involutive operators D1, ..., Dn. Though D1 ο D = 0 implies ad (D) ο ad(D1) = 0 by taking the respective adjoint operators, then ad (D) may not generate the CC of ad (D1) and measuring such ˇ°gapsˇ± led to introduce extension modules in differential homological algebra. They may also depend on the parameters and such a situation is well known in ordinary or partial control theory. When Rq is not involutive, a standard prolongation/projection (PP) procedure allows in general to find integers r, s such that the image \"\" of the projection at order q+r of the %K Differential Operator %K Adjoint Operator %K Differential Sequence %K Einstein Equations %K Kerr Metric %K Differential Module %K Extension Module %K Contact Structure %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=122456