The butterfly velocity and the Lyapunov exponent of four-dimensional rotating
charged asymptotically AdS black holes are calculated to probe chaos using
localized rotating and charged shock waves. The localized shocks also generate
butterfly velocities which quickly vanish when we approach extremality,
indicating no entanglement spread near extremality. One of the butterfly
velocity modes is well bounded by both the speed of light and the
Schwarzschild-AdS result, while the other may become superluminal. Aside from
the logarithmic behavior of the scrambling time which indicates chaos, the
Lyapunov exponent is also positive and bounded by κ=2πTH​/(1−μL). The Kerr-NUT-AdS and Kerr-Sen-AdS solutions are used
as examples to attain a better understanding of the chaotic phenomena in
rotating black holes, especially the ones with extra conserved charges.Comment: 10 pages, 4 figures. Comments are welcom