Physical objects approaching the Cauchy horizon of a rapidly rotating Kerr black hole

TL;DR

This study numerically analyzes the behavior of Weyl scalars near the Cauchy horizon of a rapidly rotating Kerr black hole and models the resulting physical object deformation, revealing resonance effects.

Contribution

It provides numerical solutions for Weyl scalars in a Kerr black hole and models object deformation, highlighting resonance phenomena at the Cauchy horizon.

Findings

Weyl scalars' amplitude and frequency match linear perturbation results

Object deformation is significant at the Cauchy horizon

Resonance occurs when driving and internal frequencies align

Abstract

We solve the 2+1-dimensional Teukolsky equation numerically for the Weyl scalars $\psi_0$ and $\psi_4$ along a time-like geodesic approaching the Cauchy horizon of a rapidly rotating perturbed Kerr black hole. We find that both the amplitude and frequency of the Weyl scalars agree with the results of linear perturbation analysis. We then model a physical object by a simple damped harmonic oscillator, which is driven by an external force that mimics the tidal force experienced by the infalling object. We use this model to find the total deformation of the object at the Cauchy horizon, and the resonant effect when the driving force's frequency matches the internal frequency of the oscillator that models the object.