Nonlinear Collapse in the Semilinear Wave Equation in AdS

Abstract

Previous studies of the semilinear wave equation in Minkowski space have shown a type of critical behavior in which large initial data collapse to singularity formation due to nonlinearities while small initial data does not. Numerical solutions in spherically symmetric Anti-de Sitter (AdS) are presented here which suggest that, in contrast, even small initial data collapse eventually. Such behavior appears analogous to the recent result of Ref. [1] that found that even weak, scalar initial data collapse gravitationally to black hole formation via a weakly turbulent instability. Furthermore, the imposition of a reflecting boundary condition in the bulk introduces a cut-off, below which initial data fails to collapse. This threshold appears to arise because of the dispersion introduced by the boundary condition.

4 pages, 5 figures, Updated with higher resolution runs; Updated with suggestions from referee and an added panel in Fig. 4; Accepted at PRD

Cited by in corpus (4)

• Non-Spherically Symmetric Collapse in Asymptotically AdS Spacetimes
• Maxwell-dilaton dynamics
• Gravitational systems in asymptotically anti-de Sitter space-times
• Universal turbulence on branes in holography