Non existence of closed null geodesics in Kerr spacetimes

The Kerr-star spacetime is the extension over the horizons and in the negative radial region of the slowly rotating Kerr black hole. It is known that below the inner horizon, there exist both timelike and null (lightlike) closed curves. Nevertheless, we prove that the null geodesics cannot be closed in the Kerr-star spacetime.Comment: 26 pages, 17 figures. Corrections: typo at p. 14 and explicit non-vanishing Christoffel symbol in Prop. 5.