The Large Dimension Limit of a Small Black Hole Instability in Anti-de Sitter Space

Understand

We study the dynamics of a black hole in an asymptotically $AdS_d \times S^d$ space-time in the limit of a large number of dimensions, $d \to \infty$.

• Such a black hole is known to become dynamically unstable below a critical radius.
• We derive the dispersion relation for the quasinormal mode that governs this instability in an expansion in $1/d$.
• We also provide a full nonlinear analysis of the instability at leading order in $1/d$.