Resonant Dynamics and the Instability of Anti-de Sitter Spacetime.
We consider spherically symmetric Einstein-massless-scalar field equations with a negative cosmological constant in five dimensions and analyze the evolution of small perturbations of anti-de Sitter (AdS) spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing the instability of AdS under arbitrarily small perturbations.
Institute of Physics, Jagiellonian University, Kraków, Poland.
Piotr
P
Bizoń
Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Golm, Germany.
Maciej
M
Maliborski
Institute of Physics, Jagiellonian University, Kraków, Poland.
Andrzej
A
Rostworowski