Fast and Slow Coherent Cascades in Anti-de Sitter Spacetime

TL;DR

This paper investigates the dynamics of small perturbations in 3+1 dimensional Anti-de Sitter spacetime, revealing coherent phase behavior and different collapse timescales, with implications for understanding gravitational stability.

Contribution

It introduces a detailed analysis of phase spectra and collapse behaviors in AdS spacetime using the Two Time Framework, identifying classes of initial conditions with distinct collapse properties.

Findings

Higher frequency modes exhibit coherent phase alignment.

Certain initial conditions lead to infinite slow-time collapse.

Energy spectrum approaches a power law with inverse frequency scaling.

Abstract

We study the phase and amplitude dynamics of small perturbations in 3+1 dimensional Anti-de Sitter spacetime using the truncated resonant approximation, also known as the Two Time Framework (TTF). We analyse the phase spectrum for different classes of initial data and find that higher frequency modes turn on with coherently aligned phases. Combining numerical and analytical results, we conjecture that there is a class of initial conditions that collapse in infinite slow time and to which the well-studied case of the two-mode, equal energy initial data belongs. We additionally study perturbations that collapse in finite time, and find that the energy spectrum approaches a power law, with the energy per mode scaling approximately as the inverse first power of the frequency.