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SAM Lectures on Extremal Black Holes in d = 4 Extended Supergravity

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The Attractor Mechanism

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 134))

Abstract

We report on recent results in the study of extremal black hole attractors in N = 2, d = 4 ungauged Maxwell–Einstein supergravities. For homogeneous symmetric scalar manifolds, the three general classes of attractor solutions with non-vanishing Bekenstein–Hawking entropy are discussed. They correspond to three (inequivalent) classes of orbits of the charge vector, which sits in the relevant symplectic representation R V of the U-duality group. Other than the \( \frac{1}{2}{- BPS} \) one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The complete classification of the U-duality orbits, as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon), is also reviewed. Finally, we consider the analogous classification for N ≥ 3-extended, d = 4 ungauged supergravities, in which also the \( \frac{1}{N}{- BPS} \) attractors yield a related moduli space.

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Acknowledgements

This work is supported in part by the ERC Advanced Grant no. 226455, “Supersymmetry, Quantum Gravity and Gauge Fields” (SUPERFIELDS).

A. M. would like to thank the William I. Fine Theoretical Physics Institute (FTPI) of the University of Minnesota, Minneapolis, MN, USA, the Center for Theoretical Physics (CTP) of the University of California, Berkeley, CA, USA, and the Department of Physics and Astronomy of the University of California, Los Angeles, CA, USA, where part of this work was done, for kind hospitality and stimulating environment. Furthermore, A. M. would like to thank Ms. Hanna Hacham for peaceful and inspiring hospitality in Palo Alto, CA, USA.

The work of S. B. has been supported in part by the grant INTAS-05-7928.

The work of S. F. has been supported also in part by INFN – Frascati National Laboratories, and by D.O.E. grant DE-FG03-91ER40662, Task C.

The work of M. G. has been supported in part by National Science Foundation under grant number PHY-0555605. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

The work of A. M. has been supported by an INFN visiting Theoretical Fellowship at SITP, Stanford University, Stanford, CA, USA.

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    Stefano Bellucci

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    Stefano Bellucci

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Bellucci, S., Ferrara, S., Günaydin, M., Marrani, A. (2010). SAM Lectures on Extremal Black Holes in d = 4 Extended Supergravity. In: Bellucci, S. (eds) The Attractor Mechanism. Springer Proceedings in Physics, vol 134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10736-8_1

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