Differential invariants of the Kerr vacuum (Q1878348)

The Kerr vacuum has two independent invariants derivable from the Riemann tensor without differentiation. The norm associated with the gradients of these scalar fields form a rather natural class of differential invariants for investigation and yet there appears to be no discussion of these in the literature. The author considers differential invariants with one differentiation (that is, invariants containing no more than three derivatives of the metric tensor). After reviewing invariants constructed directly from covariant derivatives of the Weyl tensor (and its dual), it is shown that the norms associated with the gradients of the two non-differential invariants of the Kerr vacuum locally single out the horizons, but more importantly, their global behavior reflects the background angular momentum as the volume of space allowing a timelike gradient decreases with increasing angular momentum becoming zero in the degenerate case. The nakedly singular cases allow no timelike gradients.