On the canonical energy of weak gravitational fields with a cosmological constant .

We analyse the canonical energy of vacuum linearised gravitational fields on light cones on a de Sitter, Minkowski, and Anti de Sitter backgrounds in Bondi gauge. We derive the associated asymptotic symmetries. When the energy diverges, but a renormalised formula with well defined flux is obtained.

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.

Time-periodic solutions in an Einstein AdS-massless-scalar-field system.

We construct time-periodic solutions for a system of a self-gravitating massless scalar field, with a negative cosmological constant, in d+1 spacetime dimensions at spherical symmetry, both perturbatively and numerically. We estimate the convergence radius of the formally obtained perturbative series and argue that it is greater then zero. Moreover, this estimate coincides with the boundary of the convergence domain of our numerical method and the threshold for the black-hole formation.

Instability of flat space enclosed in a cavity.

We consider a spherically symmetric self-gravitating massless scalar field enclosed inside a timelike worldtube R×S(3) with a perfectly reflecting wall. Numerical evidence is given that arbitrarily small generic initial data evolve into a black hole.