Coherent Cascade Conjecture for Collapsing Solutions in Global AdS

TL;DR

This paper investigates the nonlinear gravitational dynamics of a scalar field in AdS spacetime, proposing a coherent phase cascade model that explains black hole formation and matches numerical simulations in 4+1 dimensions.

Contribution

It introduces a coherent phase cascade framework with stationary solutions that predict black hole formation, differing from the traditional weak turbulence approach.

Findings

Stationary solutions with coherent phases and power-law spectra are found.

These spectra lead to diverging backreaction, indicating collapse.

The solutions match numerical results in 4+1 dimensions before black hole formation.

Abstract

We analyze the gravitational dynamics of a classical scalar field coupled to gravity in asymptotically AdS spacetime, which leads to black hole formation on the shortest nonlinear time scale for some initial conditions. We show that the observed collapse cannot be described by the well-known process of a random-phase cascade in the theory of weak turbulence. This implies that the dynamics on this time scale is highly sensitive to the phases of modes. We explore the alternative possibility of a coherent phase cascade and analytically find stationary solutions with completely coherent phases and power-law energy spectra. We show that these power-law spectra lead to diverging geometric backreaction, which is the likely precursor to black hole formation. In 4+1 dimensions, our stationary solution has the same power law energy spectrum as the final state right before collapse observed in numerical simulations. We conjecture that our stationary solutions describe the system shortly before collapse in other dimensions, and predict the energy spectrum.