  We analytically study the linear response of a near-extremal Kerr black hole
to external scalar, electromagnetic, and gravitational field perturbations. We
show that the energy density, electromagnetic field strength, and tidal force
experienced by infalling observers exhibit transient growth near the horizon.
The growth lasts arbitrarily long in the extremal limit, reproducing the
horizon instability of extremal Kerr. We explain these results in terms of
near-horizon geometry and discuss potential astrophysical implications.
