Extremal non-BPS black holes and entropy extremization

Abstract

At the horizon, a static extremal black hole solution in N=2 supergravity in four dimensions is determined by a set of so-called attractor equations which, in the absence of higher-curvature interactions, can be derived as extremization conditions for the black hole potential or, equivalently, for the entropy function. We contrast both methods by explicitly solving the attractor equations for a one-modulus prepotential associated with the conifold. We find that near the conifold point, the non-supersymmetric solution has a substantially different behavior than the supersymmetric solution. We analyze the stability of the solutions and the extrema of the resulting entropy as a function of the modulus. For the non-BPS solution the region of attractivity and the maximum of the entropy do not coincide with the conifold point.

19 pages, 4 figures, AMS-LaTeX, reference added

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• Stationary black holes and attractor mechanism
• Erice Lectures on Black Holes and Attractors
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• Non-supersymmetric Black Holes and Topological Strings
• Non-extremal black holes of N=2, d=4 supergravity
• d=4 Attractors, Effective Horizon Radius and Fake Supergravity
• 4d/5d Correspondence for the Black Hole Potential and its Critical Points
• d=4 Black Hole Attractors in N=2 Supergravity with Fayet-Iliopoulos Terms
• Non-BPS Attractors in 5d and 6d Extended Supergravity
• Attractors with Vanishing Central Charge
• Black hole entropy functions and attractor equations
• Attractors in Black
• On Attractor Mechanism and Entropy Function for Non-extremal Black Holes/Branes
• One entropy function to rule them all
• Moduli and (un)attractor black hole thermodynamics
• Effects of brane-flux transition on black holes in string theory
• Separation of Attractors in 1-modulus Quantum Corrected Special Geometry
• On The Stability of Non-Supersymmetric Attractors in String Theory
• On Entropy Function for Supersymmetric Black Rings
• Entropy Function for Non-Extremal Black Holes in String Theory
• Entropy function for rotating extremal black holes in very special geometry
• On the Entropy Function and the Attractor Mechanism for Spherically Symmetric Extremal Black Holes
• A Note on Exact Solutions and Attractor Mechanism for Non-BPS Black Holes
• SAM Lectures on Extremal Black Holes in d=4 Extended Supergravity
• Black hole solutions of N=2, d=4 supergravity with a quantum correction, in the H-FGK formalism
• Entropy Function for Non-extremal D1D5 and D2D6NS5-branes