Stephen R. Green

Holographic Thermalization, Stability of Anti–de Sitter Space, and the Fermi-Pasta-Ulam Paradox

For a real massless scalar field in general relativity with a negative cosmological constant, we uncover a large class of spherically symmetric initial conditions that are close to anti-de Sitter space (AdS) but whose numerical evolution does not result in black hole formation. According to the AdS/conformal field theory (CFT) dictionary, these bulk solutions are dual to states of a strongly interacting boundary CFT that fail to thermalize at late times. Furthermore, as these states are not stationary, they define dynamical CFT configurations that do not equilibrate. We develop a two-time-scale perturbative formalism that captures both direct and inverse cascades of energy and agrees with our fully nonlinear evolutions in the appropriate regime. We also show that this formalism admits a large class of quasiperiodic solutions. Finally, we demonstrate a striking parallel between the dynamics of AdS and the classic Fermi-Pasta-Ulam-Tsingou problem.

Conserved quantities and dual turbulent cascades in anti–de Sitter spacetime

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

Nonlinear Evolution and Final Fate of Charged Anti–de Sitter Black Hole Superradiant Instability

E

Islands of stability and recurrence times in AdS

of the modes: The particle number

Examples of backreaction of small scale inhomogeneities in cosmology

N

Superradiant instabilities of asymptotically anti-de Sitter black holes

and Hamiltonian

Coupled Oscillator Model for Nonlinear Gravitational Perturbations

H

Newtonian and Relativistic Cosmologies

of our TTF system. Simultaneous conservation of

How well is our universe described by an FLRW model

E

Holographic Path to the Turbulent Side of Gravity

and