Nonlinear Dynamics near the Threshold of Gravitational Collapse

Abstract

Perturbation theory is an essential tool to model and interpret gravitational dynamics, for example, binary black hole mergers. Therefore it is also crucial to precisely understand its regimes of validity. The collapse of a scalar field under its own self-gravity provides a clean laboratory to study these questions. By varying the field's initial amplitude we can transition smoothly between a perturbative regime, where the field scatters in an approximately flat spacetime; and a nonperturbative regime, where a black hole forms in finite time. In this work, we use numerical relativity simulations of this set-up to investigate the accuracy of a perturbative expansion around flat spacetime, including next-to-next-to-leading order effects. Our simulations show deviations from these perturbative predictions before black hole formation, once the maximum luminosity of the process is sufficiently large, $L_{peak} \sim 10^{-2} L_{Planck}$. We characterize these nonlinear effects including a redshift of the driving frequency and a power-law spectral amplitude, which we show is consistent with approximate discrete self-similarity. These results provide a step forward towards understanding the limits of perturbative expansions in more realistic strong-gravity phenomena such as non-spherical collapse and high-velocity black hole mergers.