title: Holographic thermalization, stability of anti-de sitter space, and the Fermi-Pasta-Ulam paradox.
abstract: 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.
authors.affiliation: Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada.
authors.forename: Venkat
authors.initials: V
authors.lastname: Balasubramanian
authors.affiliation: Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Alex
authors.initials: A
authors.lastname: Buchel
authors.affiliation: Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada.
authors.forename: Stephen R
authors.initials: SR
authors.lastname: Green
authors.affiliation: Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Luis
authors.initials: L
authors.lastname: Lehner
authors.affiliation: Department of Physics, Long Island University, Brookville, New York 11548, USA.
authors.forename: Steven L
authors.initials: SL
authors.lastname: Liebling