Chaotic Behavior of Geodesics in Kerr-like Spacetime

TL;DR

This paper investigates how test particles move in a perturbed Kerr-like spacetime, revealing chaotic behavior near the event horizon as the quadrupole moment increases, using simulations and phase space analysis.

Contribution

It introduces a study of chaos in geodesic motion within a Kerr-like metric with quadrupole perturbation, highlighting the emergence of chaos near the horizon.

Findings

Chaotic regions appear near the event horizon as quadrupole moment increases.

Rotation number analysis confirms chaos in the phase space.

Simulations demonstrate the transition from regular to chaotic motion.

Abstract

In this contribution, the motion of unitary mass test particles in a perturbed Kerr-like metric is studied using simulations in the configuration and phase space. Our metric represents the approximate exterior spacetime of a massive rotating body with mass quadrupole moment $q$. Chaotic behavior arises as the $q$ parameter increases. The rotation number is determined for an axis of symmetry in the corresponding Poincar\'e section. The existence of chaotic regions in the region near the source event horizon is shown.