Abstract
We study the basin of attraction of static extremal black holes, in the
concrete setting of the STU model. By finding a connection to a decoupled
Toda-like system and solving it exactly, we find a simple way to characterize
the attraction basin via competing behaviors of certain parameters. The
boundaries of attraction arise in the various limits where these parameters
degenerate to zero. We find that these boundaries are generalizations of the
recently introduced (extremal) subtracted geometry: the warp factors still
exhibit asymptotic integer power law behaviors, but the powers can be different
from one. As we cross over one of these boundaries ("generalized
subttractors"), the solutions turn unstable and start blowing up at finite
radius and lose their asymptotic region. Our results are fully analytic, but we
also solve a simpler theory where the attraction basin is lower dimensional and
easy to visualize, and present a simple picture that illustrates many of the
basic ideas.
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