Renormalization, averaging, conservation laws and AdS (in)stability

TL;DR

This paper investigates conservation laws in non-linear perturbations of AdS spacetime, revealing additional invariants that influence the stability and energy transfer among modes, using averaging methods for analysis.

Contribution

It identifies new conservation laws in gravitational perturbations of AdS, extending previous results and connecting dynamical and non-dynamical scalar field systems through symmetry analysis.

Findings

Discovered two new conservation laws beyond energy conservation.

Conservation laws restrict slow energy transfer between modes.

Averaging methods reveal symmetries underlying these invariants.

Abstract

We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.