Lectures on attractors and black holes

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Abstract
A basic survey on some aspects of four‐dimensional black holes (BHs) is given in these lectures. It covers thermodynamical properties as well as the Attractor Mechanism for extremal BHs in an environment of scalar field background. Some relevant formulæ for the critical points of the BH “effective potential” are discussed, and the simplest example uncovering the attractor behavior, the Maxwell‐Einstein‐dilaton supergravity, is analyzed in detail. Observations on similarities between BH entropy (as given by the Bekenstein‐Hawking entropy‐area formula) and multipartite entanglement of qubits in quantum information theory are reported, as well. Finally, among the latest developments, the moduli space of attractor points for 𝒩 ≥ 2 supergravities is also considered. Based on lectures given by S. Ferrara at the International School of Subnuclear Physics, 45th Course: Search for the “Totally Unexpected” in the LHC era, Erice, Italy, 29 August – 7 September 2007 (Directors: G. 't Hooft – A. Zichichi), and at the III Avogadro Meeting on Theoretical Physics, Alessandria, Italy, 19 – 21 December 2007.
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