Non existence of closed and bounded null geodesics in Kerr spacetimes

TL;DR

This paper proves that in Kerr-star spacetimes, null geodesics cannot be closed or confined to a compact region, clarifying the behavior of lightlike paths in these black hole models.

Contribution

It establishes the non-existence of closed and bounded null geodesics in Kerr-star spacetimes, extending understanding of geodesic behavior in rotating black hole geometries.

Findings

Null geodesics are not closed in Kerr-star spacetime.

Null geodesics cannot be contained in a compact subset.

Provides insight into lightlike path behavior in black hole extensions.

Abstract

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 null geodesics can be neither closed nor even contained in a compact subset of the Kerr-star spacetime.