Precession of angular momentum vector in a slowly rotating Kerr metric (Q1067625)

Specializing Penrose and Floyd's result \(F_{ab;c}=F_{[ab;c]}\) to the Kerr metric, we explicitly construct the skew symmetric tensor \(F_{ab}\) and Carter's quadratic integral of geodesic motion. \(F_{ab}\) is then shown to be closely related to the orbital angular momentum encountered in Newtonian mechanics. Furthermore, \(F_{ab}\) can be decomposed additively into \(L_{ab}\) and \(M_{ab}\), where \(L_{ab}\) has the character of angular momentum, and \(M_{ab}\) exists only for a nonzero rotation parameter, a, of the Kerr metric. It turns out that the equation of precession \(\dot L_ a=\phi^ b_ a L_ b\) has a nontrivial solution only for the case of a slowly rotating Kerr metric valid to first order in rotation parameter. In this case, Carter's integral can be interpreted as the squared length of the precessing angular momentum vector \(L_ a=L^ b_ a P_ b\). The equation of precession is solved, and a vector \(\Omega^ a\) describing angular velocity of precession is derived.