On weakly turbulent instability of anti-de Sitter space

Abstract

We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) spacetime by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS spacetime is unstable under arbitrarily small generic perturbations. We conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies.

4 pages, 4 figures. Oops, in the previous versions the values of parameters of initial data and horizon radii were given by mistake in units used by us in numerical simulations $\ell =2/\pi$, instead of $\ell =1$. This mistake in Eq.(9) is corrected and the vertical axis in Fig.1 is rescaled accordingly

References in corpus (1)

• On the uniqueness and global dynamics of AdS spacetimes

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