Ultraviolet asymptotics and singular dynamics of AdS perturbations
arXiv:1508.04943 · doi:10.1007/JHEP10(2015)079
Abstract
Important insights into the dynamics of spherically symmetric AdS-scalar field perturbations can be obtained by considering a simplified time-averaged theory accurately describing perturbations of amplitude epsilon on time-scales of order 1/epsilon^2. The coefficients of the time-averaged equations are complicated expressions in terms of the AdS scalar field mode functions, which are in turn related to the Jacobi polynomials. We analyze the behavior of these coefficients for high frequency modes. The resulting asymptotics can be useful for understanding the properties of the finite-time singularity in solutions of the time-averaged theory recently reported in the literature. We highlight, in particular, the gauge dependence of this asymptotics, with respect to the two most commonly used gauges. The harsher growth of the coefficients at large frequencies in higher-dimensional AdS suggests strengthening of turbulent instabilities in higher dimensions. In the course of our derivations, we arrive at recursive relations for the coefficients of the time-averaged theory that are likely to be useful for evaluating them more efficiently in numerical simulations.
15 pages; v4: typos in equation (33) corrected
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- AdS nonlinear instability: moving beyond spherical symmetry
- Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations
- A nonrelativistic limit for AdS perturbations
- Moving Closer to the Collapse of a Massless Scalar Field in Spherically Symmetric Anti-de Sitter Spacetimes
- Classes of Stable Initial Data for Massless and Massive Scalars in Anti-de Sitter Spacetime
- Necessary conditions for an AdS-type instability
- Two worlds collide: Interacting shells in AdS spacetime and chaos
- Black Hole Formation in AdS Einstein-Gauss-Bonnet Gravity
- AdS nonlinear instability: breaking spherical and axial symmetries
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- New islands of stability with double-trace deformations
- Fast and Slow Coherent Cascades in Anti-de Sitter Spacetime
- Detailed ultraviolet asymptotics for AdS scalar field perturbations
- Examining Instabilities Due to Driven Scalars in AdS
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- The instability of anti-de Sitter space-time
- Phase Diagram of Stability for Massive Scalars in Anti-de Sitter Spacetime
- Gravitational systems in asymptotically anti-de Sitter space-times
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