Supersymmetry and Attractors

Abstract

We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the moduli space (a minimum corresponds to a fixed point of attraction). The extremal value of the square of the central charge provides the area of the horizon, which depends only on electric and magnetic charges. The doubling of unbroken supersymmetry at the fixed point of attraction for N=2 black holes near the horizon is derived via conformal flatness of the Bertotti-Robinson-type geometry. These results provide an explicit model independent expression for the macroscopic Bekenstein-Hawking entropy of N=2 black holes which is manifestly duality invariant. The presence of hypermultiplets in the solution does not affect the area formula. Various examples of the general formula are displayed. We outline the attractor mechanism in N=4,8 supersymmetries and the relation to the N=2 case. The entropy-area formula in five dimensions, recently discussed in the literature, is also seen to be obtained by extremizing the 5d central charge.

20 pages, 2 figures, LaTeX. few misprints removed, version to appear in Phys. Rev. D

References in corpus (8)

• D-brane Approach to Black Hole Quantum Mechanics
• D--branes and Spinning Black Holes
• Macroscopic Entropy of $N=2$ Extremal Black Holes
• Solitonic Strings and BPS Saturated Dyonic Black Holes
• E(7) Symmetric Area of the Black Hole Horizon
• N=2 Heterotic Superstring and its Dual Theory in Five Dimensions
• Internal Structure of Black Holes
• Extremal Black Holes as Bound States

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• Multi-centered $\mathcal{N}=2$ BPS black holes: a double copy description
• Qubits and STU Black Holes with Eight Electric and Magnetic Charges
• A note on non-linear electrodynamics, regular black holes and the entropy function
• Indefinite theta functions for counting attractor backgrounds
• Supersymmetric near-horizon geometries in D = 6 supergravity: Lichnerowicz theorems, index theory and symmetry enhancement
• Backreaction I: The Torus
• Black holes, first-order flow equations and geodesics on symmetric spaces
• A T-Fold Black Hole in Doubled Type IIB
• Towards the Core of the Quantum Monopole
• Gauss-Bonnet Contributions to the Entropy of Extremal Black Holes in the Gauge-Gravity sector
• Black holes in the Superworld
• The linear relations between the complex moduli and using the linear relations reduce the stabilization equations for supersymmetric black holes in N=2 theory
• Gravitational collapse and entropy of Black Holes with magnetic sources