Nonlinear Collapse in the Semilinear Wave Equation in AdS
arXiv:1212.6970 · doi:10.1103/PhysRevD.87.081501
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.
arXiv comment4 pages, 5 figures, Updated with higher resolution runs; Updated with suggestions from referee and an added panel in Fig. 4; Accepted at PRD
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- Non-Spherically Symmetric Collapse in Asymptotically AdS Spacetimes
- Coherent Cascade Conjecture for Collapsing Solutions in Global AdS
- Multiple critical gravitational collapse of charged scalar with reflecting wall
- Maxwell-dilaton dynamics
- Gravitational systems in asymptotically anti-de Sitter space-times
- Universal turbulence on branes in holography