Abstract
We consider the classification of near-horizon geometries in a general
two-derivative theory of gravity coupled to abelian gauge fields and uncharged
scalars in four and five dimensions, with one and two commuting rotational
symmetries respectively. Assuming that the theory of gravity reduces to a 3d
non-linear sigma model (as is typically the case for ungauged supergravities),
we show that the functional form of any such near-horizon geometry may be
determined. As an example we apply this to five dimensional minimal
supergravity. We also construct an example of a five parameter near-horizon
geometry solution to this theory with S^1 X S^2 horizon topology. We conjecture
that certain four parameter subsets correspond to the near-horizon geometries
of yet to be constructed extremal black rings with both electric and dipole
charges.
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