Butterfly in Spacetime: Inherent Instabilities in Stable Black Holes

TL;DR

This study demonstrates that small local perturbations near a black hole's horizon can destabilize it, indicating extreme sensitivity of black hole stability to near-horizon geometry and quantum fluctuations.

Contribution

It introduces a numerical approach to test black hole stability against localized horizon perturbations, revealing potential instabilities not previously understood.

Findings

Infinitesimal deformations can overturn black hole stability

Certain stabilizing deformations in flat space destabilize black holes

Quantum fluctuations near the horizon can trigger instability

Abstract

This paper numerically studies if the stability of a stable black hole is robust against the small perturbation on geometry near its event horizon. As a toy model, it encodes the such perturbation into deformations of Regge-Wheeler potential. It considers three different types of local deformations-the negative static bump potential, the stochastic potential and bump potential modulated by time function in low frequency limit. Our numerical results show that infinitesimal local deformations on Regge-Wheeler potential near the horizon can overturn stability of a stable black hole, implying that late-time behavior of a stable black hole is extremely sensitive to geometry near horizon. Specially, certain deformations that stabilize systems in flat backgrounds can destabilize otherwise stable black holes. It also shows that horizon-induced redshift transforms near-horizon quantum fluctuations into classical-scale stochastic deformations capable of triggering instability, implying that even an isolated black hole cannot keep stable in extended timescales.