Early-Time Nonlinear Growth in an Unstable Q-Ball Hairy Black Hole

TL;DR

This paper demonstrates that during the early growth phase of an unstable Q-ball hairy black hole, nonlinear effects can dominate the evolution of certain scalar field components, deviating from linear instability predictions.

Contribution

It reveals that the early-time growth of scalar field components in an unstable black hole can be dominated by second-order effects, challenging the assumption that linear modes govern initial evolution.

Findings

Linear unstable QNM has a larger amplitude in one scalar component.

Early growth of the weaker component is dominated by a second-order QNM.

Results show nonlinear effects can dominate during perturbative evolution.

Abstract

Early-time evolution away from an unstable equilibrium in a nonlinear system is often expected to be governed by the associated linear instability. Combining full nonlinear evolution with first- and second-order quasinormal mode (QNM) calculations, we show that this expectation can fail during the unstable growth stage of a Q-ball hairy black hole in Einstein-Maxwell theory with a charged self-interacting scalar field. The linear unstable QNM has a much larger amplitude in one component of the scalar field than in the other: the more strongly responding component follows that mode, whereas the early growth of the more weakly responding component is dominated by a second-order QNM sourced by the linear unstable mode. This occurs while the evolution remains perturbative. Our results thus show that the early growth of an individual component need not be governed by its linear response.