Geodesic causality in Kerr spacetimes with $|a|\ge M$

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 $|a|>M$, meaning that through every point there exists a closed timelike curve. Despite this, we prove that the Kerr spacetimes do not admit any closed null geodesics when $|a|\ge M$. This result generalises recent findings by one of the authors, which showed the nonexistence of closed causal geodesics in the case $|a|<M$. Combining these results, we establish the absence of closed null geodesics in Kerr spacetimes for any non-zero $a$.

References in corpus (4)

• Naked Singularities in Spherically Symmetric Inhomogeneous Tolman-Bondi Dust Cloud Collapse
• Strong curvature naked singularities in spherically symmetric perfect fluid collapse
• Nonexistence of closed timelike geodesics in Kerr spacetimes
• Non existence of closed and bounded null geodesics in Kerr spacetimes