Geodesic causality in Kerr spacetimes with |a| ≥ M

Abstract

The analytic extension of the Kerr spacetimes into the negative radial region contains closed causal curves for any non-zero rotation parameter a and mass parameter M. Furthermore, the spacetimes become totally vicious when $\left|a\right|>M$, meaning that through every point there exists a closed timelike curve. Despite this, we prove that Kerr spacetimes do not admit any closed null geodesics when $\left|a\right|\ge M$. This result generalises recent findings by one of the authors, which showed the nonexistence of closed causal geodesics in the case $\left|a\right|<M$. Combining these results, we establish the absence of closed null geodesics in Kerr spacetimes for any non-zero a.