A Space/Time Interchange Symmetry of Rotating AdS Black Holes in General Dimensions

We revisit the previously known local inversion symmetry of the five-dimensional Kerr-AdS metric that relates the over-rotating black hole to the under-rotating one and reinterpret it as an interchanging symmetry between time and the longitudinal angular coordinates. We generalize this to all $D$ dimensions, including $D=4$, thereby enlarging the trivial linear ${\mathbb{Z}}_N$ symmetry of the $N=\lfloor (D-1)\mathrm{/}2\rfloor$ longitudinal angular coordinates to the nonlinearly realized ${\mathbb{Z}}_{N+1}$ symmetry that involves time.