Nonexistence of closed timelike geodesics in Kerr spacetimes

TL;DR

This paper proves that in Kerr-star spacetimes, despite closed timelike curves existing below the inner horizon, no closed timelike geodesics can occur, extending previous results on null geodesics.

Contribution

It establishes the nonexistence of closed timelike geodesics in Kerr-star spacetimes, complementing prior work on null geodesics and clarifying causal structure.

Findings

No closed timelike geodesics in Kerr-star spacetime

Closed null geodesics are also absent

Supports the causal stability of Kerr-star spacetime

Abstract

The Kerr-star spacetime is the extension over the horizons and in the negative radial region of the Kerr spacetime. Despite the presence of closed timelike curves below the inner horizon, we prove that the timelike geodesics cannot be closed in the Kerr-star spacetime. Since the existence of closed null geodesics was ruled out by the author in Sanzeni [arXiv:2308.09631v3 (2024)], this result shows the absence of closed causal geodesics in the Kerr-star spacetime.