The Hesse potential, the c-map and black hole solutions

A bstract We present a new formulation of the local c -map, which makes use of a symplectically covariant real formulation of special Kähler geometry. We obtain an explicit and simple expression for the resulting quaternionic, or, in the case of reduction over time, para-quaternionic Kähler metric i...

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Bibliographic Details
Published in:The journal of high energy physics 2012-07, Vol.2012 (7), Article 163
Main Authors: Mohaupt, T., Vaughan, O.
Format: Article
Language:English
Subjects:
Black holes
Classical and Quantum Gravitation
Elementary Particles
High energy physics
Manifolds (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
Rotation
String Theory
Supersymmetry
Symmetry
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Summary:A bstract We present a new formulation of the local c -map, which makes use of a symplectically covariant real formulation of special Kähler geometry. We obtain an explicit and simple expression for the resulting quaternionic, or, in the case of reduction over time, para-quaternionic Kähler metric in terms of the Hesse potential, which is similar to the expressions for the metrics obtained from the rigid r - and c -map, and from the local r -map. As an application we use the temporal version of the c -map to derive the black hole attractor equations from geometric properties of the scalar manifold, without imposing supersymmetry or spherical symmetry. We observe that for general (non-symmetric) c -map spaces static BPS solutions are related to a canonical family of totally isotropic, totally geodesic submanifolds. Static non-BPS solutions can be obtained by applying a field rotation matrix which is subject to a non-trivial compatibility condition. We show that for a class of prepotentials, which includes the very special (‘cubic’) prepotentials as a subclass, axion-free solutions always admit a non-trivial field rotation matrix.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP07(2012)163