Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fake Superpotential for Large and Small Extremal Black Holes   We consider the fist order, gradient-flow, description of the scalar fields
coupled to spherically symmetric, asymptotically flat black holes in extended
supergravities. Using the identification of the fake superpotential with
Hamilton's characteristic function we clarify some of its general properties,
showing in particular (besides reviewing the issue of its duality invariance)
that W has the properties of a Liapunov's function, which implies that its
extrema (associated with the horizon of extremal black holes) are
asymptotically stable equilibrium points of the corresponding first order
dynamical system (in the sense of Liapunov). Moreover, we show that the fake
superpotential W has, along the entire radial flow, the same flat directions
which exist at the attractor point. This allows to study properties of the ADM
mass also for small black holes where in fact W has no critical points at
finite distance in moduli space. In particular the W function for small non-BPS
black holes can always be computed analytically, unlike for the large
black-hole case.

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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: gr-qc