We study the connection between many-body quantum chaos and energy dynamics
for the holographic theory dual to the Kerr-AdS black hole. In particular, we
determine a partial differential equation governing the angular profile of
gravitational shock waves that are relevant for the computation of out-of-time
ordered correlation functions (OTOCs). Further we show that this shock wave
profile is directly related to the behaviour of energy fluctuations in the
boundary theory. In particular, we demonstrate using the Teukolsky formalism
that at complex frequency $\omega_* = i 2 \pi T$ there exists an extra ingoing
solution to the linearised Einstein equations whenever the angular profile of
metric perturbations near the horizon satisfies this shock wave equation. As a
result, for metric perturbations with such temporal and angular profiles we
find that the energy density response of the boundary theory exhibit the
signatures of "pole-skipping" - namely, it is undefined, but exhibits a
collective mode upon a parametrically small deformation of the profile.
Additionally, we provide an explicit computation of the OTOC in the equatorial
plane for slowly rotating large black holes, and show that its form can be used
to obtain constraints on the dispersion relations of collective modes in the
dual CFT.