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Abstract |
Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of
a black hole are determined by scattering processes near the horizon. This prompts
the question to what extent OTOCs display chaotic behaviour in horizonless
microstate geometries. This question is complicated by the fact that Lyapunov
growth of OTOCs requires nonzero temperature, whereas constructions of microstate
geometries have been mostly restricted to extremal black holes.
We compute OTOCs for a class of extremal black holes, namely maximally rotating
BTZ black holes, and show that on average they display "slow scrambling",
characterized by cubic (rather than exponential) growth. Superposed on this
average power-law growth is a sawtooth pattern, whose steep parts correspond to
brief periods of Lyapunov growth associated to the nonzero temperature of the
right-moving degrees of freedom in a dual conformal field theory.
Next we study the extent to which these OTOCs are modified in certain
"superstrata", horizonless microstate geometries corresponding to these black
holes. Rather than an infinite throat ending on a horizon, these geometries have a
very deep but finite throat ending in a cap. We find that the superstrata display
the same slow scrambling as maximally rotating BTZ black holes, except that for
large enough time intervals the growth of the OTOC is cut off by effects related
to the cap region, some of which we evaluate explicitly. |
