Chaotic dynamics of pulsating spheres orbiting black holes

TL;DR

This paper investigates how pulsating, spinless bodies can exhibit chaotic motion around black holes in various gravity theories, using mathematical analysis to identify conditions leading to chaos.

Contribution

It demonstrates that pulsating spherical bodies can have chaotic trajectories in spherically symmetric spacetimes, extending understanding of chaos in gravitational systems.

Findings

Chaotic behavior occurs in pulsating bodies orbiting black holes.

Homoclinic intersections indicate chaos due to oscillating radii.

Analysis includes Reissner-Nordström and Ayón-Beato-García black holes.

Abstract

We study the chaotic dynamics of spinless extended bodies in a wide class of spherically symmetric spacetimes, which encompasses black-hole scenarios in many modified theories of gravity. We show that a spherically symmetric pulsating ball may have chaotic motion in this class of spacetimes. The cases of the Reissner-Nordstr{\"o}m and Ay{\'o}n-Beato-Garc{\'i}a black holes are analyzed in detail. The equations of motion for the extended bodies are obtained according to Dixon's formalism, up to quadrupole order. Then, we use Melnikov's method to show the presence of homoclinic intersections, which imply chaotic behavior, as a consequence of our assumption that the test body has an oscillating radius.