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arXiv · hep-th/0612225

Black hole entropy functions and attractor equations

G. L. Cardoso·B. de Wit·S. Mahapatra
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Abstract

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N=2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions.

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G. L. Cardoso, B. de Wit, S. Mahapatra. 2007-03-21. Black hole entropy functions and attractor equations. https://doi.org/10.1088/1126-6708%2F2007%2F03%2F085

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