New form of the Kerr solution

A new form of the Kerr solution is presented. The solution involves a time coordinate which represents the local proper time for free-falling observers on a set of simple trajectories. Many physical phenomena are particularly clear when related to this time coordinate. The chosen coordinates also ensure that the solution is well behaved at the horizon. The solution is well suited to the tetrad formalism and a convenient null tetrad is presented. The Dirac Hamiltonian in a Kerr background is also given and, for one choice of tetrad, it takes on a simple, Hermitian form.