Resonant Dynamics and the Instability of Anti–de Sitter Spacetime

2015/06/11 by Piotr Bizoń, Maciej Maliborski, Andrzej Rostworowski · 100 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #De Sitter space #De Sitter universe #Dynamics (music) #Instability #Mathematical physics #Physics #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Quantum mechanics #Spacetime #Universe #de Sitter invariant special relativity #gr-qc #hep-th #math.AP

paper · pdf · doi:10.1103/physrevlett.115.081103

published in Physical Review Letters 115(8), 081103 (American Physical Society) · 5 pages, 7 figures

arxiv created 2015/06/11 · openalex publication_date 2015/08/21 · arxiv updated 2015/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Universality and scaling in gravitational collapse of a massless scalar field

Cited by

• Classes of stable initial data for massless and massive scalars in Anti-de Sitter spacetime
• Gravitational systems in asymptotically anti-de Sitter space-times
• Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes