Chaotic dynamics of a spinless axisymmetric extended body around a Schwarzschild black hole

TL;DR

This paper explores how shape oscillations in a spinless extended body orbiting a Schwarzschild black hole can induce chaotic motion, using Dixon's formalism and Melnikov's method to analyze long-term dynamics.

Contribution

It introduces a novel analysis of chaos in extended bodies' orbits around black holes due to shape oscillations, extending previous point-particle models.

Findings

Shape oscillations can trigger chaos in orbital dynamics.

Chaotic behavior verified using Melnikov's method.

Long-term orbital deviations depend on body's shape oscillation.

Abstract

We investigate the long-term orbital dynamics of spinless extended bodies in Schwarzschild geometry, and show that periodic deviations from spherical symmetry in the shape of a test body may trigger the onset of chaos. We do this by applying Dixon's formalism at quadrupolar order to a nearly spherical body whose shape oscillates between a prolate and an oblate spheroid. The late-time chaotic behavior is then verified by applying Melnikov's method.