Conserved quantities and dual turbulent cascades in Anti-de Sitter spacetime

Understand

We consider the dynamics of a spherically symmetric massless scalar field coupled to general relativity in Anti--de Sitter spacetime in the small-amplitude limit.

• Within the context of our previously developed two time framework (TTF) to study the leading self-gravitating effects, we demonstrate the existence of two new conserved quantities in addition to the known total energy $E$ of the modes: The particle number $N$ and Hamiltonian $H$ of our TTF system.
• Simultaneous conservation of $E$ and $N$ implies that weak turbulent processes undergo dual cascades (direct cascade of $E$ and inverse cascade of $N$ or vice versa).
• This partially explains the observed dynamics of 2-mode initial data.