A space/time interchange symmetry of rotating AdS black holes in general dimensions

Abstract

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 ZN symmetry of the N=⌊(D−1)/2⌋ longitudinal angular coordinates to the nonlinearly realized ZN+1 symmetry that involves time.