Supersymmetric Rotating Black Holes and Causality Violation

TL;DR

This paper analyzes the causal structure and wave scattering of supersymmetric rotating black holes in five dimensions, revealing geodesic completeness, naked closed timelike curves, and properties of wave absorption.

Contribution

It provides the first detailed analysis of the causal structure and wave scattering properties of supersymmetric rotating black holes in five dimensions, including their maximal extension and geodesic behavior.

Findings

Spacetime is geodesically complete and free of singularities despite naked closed timelike curves.

Absorption cross-section at low frequencies equals the black hole area.

High-frequency wave dependence on angular quantum numbers.

Abstract

The geodesics of the rotating extreme black hole in five spacetime dimensions found by Breckenridge, Myers, Peet and Vafa are Liouville integrable and may be integrated by additively separating the Hamilton-Jacobi equation. This allows us to obtain the St\"ackel-Killing tensor. We use these facts to give the maximal analytic extension of the spacetime and discuss some aspects of its causal structure. In particular, we exhibit a `repulson'-like behaviour occuring when there are naked closed timelike curves. In this case we find that the spacetime is geodesically complete (with respect to causal geodesics) and free of singularities. When a partial Cauchy surface exists, we show, by solving the Klein-Gordon equation, that the absorption cross-section for massless waves at small frequencies is given by the area of the hole. At high frequencies a dependence on the angular quantum numbers of the wave develops. We comment on some aspects of `inertial time travel' and argue that such time machines cannot be constructed by spinning up a black hole with no naked closed timelike curves.