On the stability of anti-de Sitter spacetime
  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 AdS 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 instability of anti-de Sitter space by Bizon 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, much work is still to be done. The recent work of Moschidis is encouraging that it is possible to understand the problem analytically. 
Nils Deppe
gr-qc hep-th