Killing Operator for the Kerr Metric

When D: E → F is a linear differential operator of order q between the sections vector bundles over manifold X dimension n, it defined by bundle map Φ: Jq(E) F=F0 that may depend, explicitly or implicitly, on constant parameters a, b, c, ... . A “direct problem” to find generating compatibility conditions (CC) in form an D1: F0 F1. D involutive, when corresponding system Rq = ker (Φ) this procedure provides successive first involutive operators D1, ..., Dn. Though D1 ο 0 implies ad (D) ad(D1) taking respective adjoint operators, then not generate CC (D1) and measuring such “gaps” led introduce extension modules homological algebra. They also depend situation well known ordinary partial control theory. standard prolongation/projection (PP) allows general integers r, s image projection at q+r prolongation but highly parameters. However, sometimes resulting no longer depends do because they sequence used for their definition. The purpose paper study above problems Kerr (m, a), Schwarzschild 0) Minkowski (0, while computing dimensions inclusions Killing operators. Other striking motivating examples are presented.