Resonant dynamics in higher dimensional anti–de Sitter spacetime

Abstract

We present results from a detailed study of spherically symmetric Einstein-massless-scalar field dynamics with a negative cosmological constant in four to nine spacetime dimensions. This study is the first to present a detailed examination of the dynamics in anti--de Sitter beyond five dimensions, including a detailed comparison with numerical solutions of perturbative methods and their gauge dependence. Using these perturbative methods, we provide evidence that the oscillatory divergence of the first derivative used to argue for the instability of anti--de Sitter space by Bizo\ifmmode \acute{n}\else \'{n}\fi{} et al. is a gauge-dependent effect in five spacetime dimensions but the divergence of the second derivative is gauge independent. We find that the divergence of the first derivative appears to be gauge independent in higher dimensions; however, understanding how this divergence depends on the initial data is more difficult. We also find that four dimensions is more difficult to study than higher dimensions. The results we present show that while much progress has been made in understanding the rich dynamics and stability of anti--de Sitter space, there is still much work to be done. The recent work of Moschidis supports the idea that it is possible to understand the problem analytically.