Abstract
We present the main features of the physics of extremal black holes embedded in supersymmetric theories of gravitation, with a detailed analysis of the attractor mechanism for BPS and non-BPS black-hole solutions in four dimensions.
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References
B. De Witt, C. De Witt eds.: Black Holes(Gordon and Breach, New York, 1973); S. W. Hawking, W. Israel: General Relativity(Cambridge University Press, Cambridge, 1979); R. M.Wald: General Relativity(University of Chicago Press, Chicago, 1984)
G. W. Moore: Les Houches lectures on strings and arithmetic, arXiv:hepth/0401049; M. R. Douglas, R. Reinbacher, S. T. Yau: Branes, bundles and attractors: Bogomolov and beyond, arXiv:math.ag/0604597
M. J. Du.: String triality, black-hole entropy and Cayley’s hyperdeterminant, arXiv:hep-th/0601134; R. Kallosh, A. Linde: Phys. Rev. D 73, 104033 (2006) P. Levay: Phys. Rev. D 74, 024030 (2006) M. J. Du., S. Ferrara: E7 and the tripartite entanglement of seven qubits, arXiv:quant-ph/0609227; P. Levay: Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane, arXiv:hep-th/0610314
S. W. Hawking, R. Penrose: Proc. Roy. Soc. Lond. A 314, 529 (1970)
G. Gibbons: in Uni.ed theories of Elementary Particles. Critical Assessment and Prospects, Proceedings of the Heisemberg Symposium, Müunchen, Germany, 1981, ed. by P. Breitenlohner, H. P. Düurr, Lecture Notes in Physics, Vol. 160 (Springer-Verlag, Berlin, 1982); G. W. Gibbons: in Supersymmetry, Supergravity and Related Topics, Proceedings of the XVth GIFT International Physics (Girona, Spain 1984), ed. by F. del Aguila, J. de Azc’arraga, L. Ibánez, (World Scienti.c, Singapore, 1985), p. 147; P. Breitenlohner, D. Maison, G. W. Gibbons: Commun. Math. Phys. 120, 295 (1988); R. Kallosh, A. D. Linde, T. Ortin, A. W. Peet, A. Van Proeyen: Phys. Rev. D 46, 5278 (1992); R. Kallosh, T. Ortin, A. W. Peet: Phys. Rev. D 47, 5400 (1993); R. Kallosh: Phys. Lett. B 282, 80 (1992); R. Kallosh, A. W. Peet: Phys. Rev. D 46, 5223 (1992); R. R. Khuri, T. Ortin: Nucl. Phys. B 467, 355 (1996); A. Sen: Nucl. Phys. B 440, 421 (1995); A. Sen: Phys. Lett. B 303, 22 (1993); A. Sen: Mod. Phys. Lett. A 10, 2081 (1995); M. Cvetic, C. M. Hull: Nucl. Phys. B 480, 296 (1996); M. Cvetic, I. Gaida: Nucl. Phys. B 505, 291 (1997); M. Cvetic, D. Youm: arXiv:hepth/9512127; M. Cvetic, A. A. Tseytlin: Phys. Rev. D 53, 5619 (1996)
For reviews on black holes in superstring theory see: J. M. Maldacena: Black-Holes in String Theory, hep-th/9607235; A. W. Peet: TASI lectures on black holes in string theory, arXiv:hep-th/0008241; B. Pioline: Class. Quant. Grav. 23, S981 (2006); A. Dabholkar: Class. Quant. Grav. 23, S957 (2006)
S. W. Hawking: Phys. Rev. Lett. 26, 1344 (1971); J. D. Bekenstein: Phys. Rev. D 7, 2333 (1973)
A. Strominger, C. Vafa: Phys. Lett. B 379, 99 (1996); C. G. . Callan, J. M. Maldacena: Nucl. Phys. B 472, 591 (1996); G. T. Horowitz, A. Strominger: Phys. Rev. Lett. 77, 2368 (1996); R. Dijkgraaf, E. P. Verlinde, H. L. Verlinde: Nucl. Phys. B 486, 77 (1997); D. M. Kaplan, D. A. Lowe, J. M. Maldacena, A. Strominger: Phys. Rev. D 55, 4898 (1997); J. M. Maldacena: Phys. Lett. B 403, 20 (1997); J. M. Maldacena, A. Strominger, E. Witten: JHEP 9712, 002 (1997); M. Bertolini, M. Trigiante: JHEP 0010, 002 (2000)
E. Witten: Nucl. Phys. B 443, 85 (1995)
C. M. Hull, P. K. Townsend: Nucl. Phys. B 438, 109 (1995)
G. Nordstrüom: Proc. Kon. Ned. Akad. Wet. 20, 1238 (1918); H. Reissner: Ann. Physik 50, 106 (1916)
R. Penrose: Riv. Nuovo Cim. 1, 252 (1969); Gen. Rel. Grav. 34, 1141 (2002); R. Penrose: in General Relativity, an Einstein Centenary Survey,ed. by S. W. Hawking, W. Israel (Cambridge University Press, Cambridge, 1979)
B. Bertotti: Phys. Rev. 116, 1331 (1959); I. Robinson: Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 7, 351 (1959)
R. Kallosh, T. Ortin: Phys. Rev. D 48, 742 (1993); E. Bergshoe., R. Kallosh, T. Ortin: Nucl. Phys. B 478, 156 (1996)
The literature on this topic is quite extended. As a general review, see the lecture notes: K. Stelle: Lectures on Supergravity p-Branes, presented at 1996 ICTP Summer School, Trieste, arXiv:hep-th/9701088
M. J. Du., R. R. Khuri, J. X. Lu: String solitons, Phys. Rep. 259, 213 (1995)
For recent reviews see: J. H. Schwarz: Nucl. Phys. Proc. Suppl. B 55, 1 (1997); M. J. Du.: Int. J. Mod. Phys. A 11, 5623 (1996); A. Sen: Nucl. Phys. Proc. Suppl. 58, 5 (1997)
J. H. Schwarz, A. Sen, Phys. Lett. B 312, 105 (1993); J. H. Schwarz, A. Sen: Nucl. Phys. B 411, 35 (1994)
M. Gasperini, J. Maharana, G. Veneziano: Phys. Lett. B 272, 277 (1991); J. Maharana, J. H. Schwarz: Nucl. Phys. B 390, 3 (1993)
J. H. Schwarz: M theory extensions of T duality, arXiv:hep-th/9601077; C. Vafa: Nucl. Phys. B 469, 403 (1996)
S. Ferrara, R. Kallosh, A. Strominger: Phys. Rev. D 52, 5412 (1995)
S. Ferrara, R. Kallosh: Phys. Rev. D 54, 1514 (1996); S. Ferrara, R. Kallosh: Phys. Rev. D 54, 1525 (1996)
A. Strominger: Phys. Lett. B 383, 39 (1996)
J. Polchinski, Y. Cai: Nucl. Phys. B 296, 91 (1988); C. G. . Callan, C. Lovelace, C. R. Nappi, S. A. Yost: Nucl. Phys. B 308, 221 (1988); A. Sagnotti: Open strings and their symmetry groups, Cargese Summer Inst. (1987) 0521, arXiv:hep-th/0208020; M. Bianchi, A. Sagnotti: Phys. Lett. B 247, 517 (1990); M. Bianchi, A. Sagnotti: Nucl. Phys. B 361, 519 (1991); P. Horava: Nucl. Phys. B 327, 461 (1989); J. Polchinski: Phys. Rev. Lett. 75, 4724 (1995)
S. Ferrara, J. M. Maldacena: Class. Quant. Grav. 15, 749 (1998); S. Ferrara, M. Gunaydin: Int. J. Mod. Phys. A 13, 2075 (1998) 726 L. Andrianopoli et al.
L. Andrianopoli, R. D’Auria, S. Ferrara: Phys. Lett. B 403, 12 (1997)
R. M. Wald: Phys. Rev. D 48, 3427 (1993)
G. Lopes Cardoso, B. de Wit, T. Mohaupt: Phys. Lett. B 451, 309 (1999); G. Lopes Cardoso, B. de Wit, T. Mohaupt: Nucl. Phys. B 567, ) 87 (2000)
H. Ooguri, A. Strominger, C. Vafa: Phys. Rev. D 70, 106007 (2004)
R. R. Khuri, T. Ortin: Phys. Lett. B 373, 56 (1996); T. Ortin: Phys. Lett. B 422, 93 (1998); T. Ortin: Non-supersymmetric (but) extreme black holes, scalar hair and other open problems, arXiv:hep-th/9705095
S. Ferrara, G. W. Gibbons, R. Kallosh: Nucl. Phys. B 500, 75 (1997)
K. Goldstein, N. Iizuka, R. P. Jena, S. P. Trivedi: Phys. Rev. D 72, 124021 (2005)
R. Kallosh: JHEP 0512, 022 (2005)
P. K. Tripathy, S. P. Trivedi: JHEP 0603, 022 (2006)
A. Giryavets: JHEP 0603, 020 (2006)
R. Kallosh, N. Sivanandam, M. Soroush: JHEP 0603, 060 (2006)
A. Dabholkar, A. Sen, S. Trivedi: Black hole microstates and attractor without supersymmetry, arXiv:hep-th/0611143
G. G. Gibbons: http://www.lpthe.jussieu.fr/sugra30/TALKS/Gibbons.pdf, talk presented at the conference 30 years of Supergravity, journée Joüel Scherk, held in Paris the 18/10/2006
M. K. Gaillard, B. Zumino: Nucl. Phys. B 193, 221 (1981)
R. Kallosh: From BPS to non-BPS black holes canonically, arXiv:hepth/0603003
For a review, see for instance: S. Bellucci, S. Ferrara, A. Marrani: Supersymmetric Mechanics P Vol. 2: The Attractor Mechanism and Space Time Singularities, Lecture Notes in Physics, Vol. 701 (Springer, Berlin/Heidelberg, 2006), Proceedings of the SSM05–Winter School on Modern Trends in supersymmetric Mechanics, INFN-LNF, Italy (2005)
G. Lopes Cardoso, B. de Wit, J. Kappeli, T. Mohaupt: JHEP 0412, 075 (2004)
A. Sen: JHEP 0509, 038 (2005)
L. Andrianopoli, R. D’Auria, S. Ferrara, M. A. Lledo: Nucl. Phys. B 640, 46 (2002)
B. Zumino: J.Math.Phys. 3, 1055 (1962)
E. Witten, D. I. Olive: Phys. Lett. B 78, 97 (1978)
For a review on supergravity see for example: L. Castellani, R. D’Auria, P. Fré, Supergravity and Superstring Theory: A Geometric Perspective(World Scienti .c, Singapore, 1990)
E. Cremmer: in Supergravity ’81, ed. by S. Ferrara, J. G. Taylor, p. 313; B. Julia: in Superspace & Supergravity, ed. by S. Hawking, M. Rocek (Cambridge, 1981) p. 331
A. Salam, E. Sezgin: Supergravities in Diverse Dimensions, ed. by A. Salam, E. Sezgin (North-Holland, World Scienti.c, 1989), Vol. 1
L. Andrianopoli, R. D’Auria, S. Ferrara: Int. J. Mod. Phys. A 13, 431 (1998)
L. Andrianopoli, R. D’Auria, S. Ferrara: Int. J. Mod. Phys. A 12, 3759 (1997)
L. Castellani, A. Ceresole, S. Ferrara, R. D’Auria, P. Fré, E. Maina: Nucl. Phys. B 268, 317 (1986)
E. Bergshoe., I. G. Koh, E. Sezgin: Phys. Lett. B 155, 71 (1985); M. de Roo, P. Wagemans: Nucl. Phys. B 262, 644 (1985)
S. Ferrara, R. Kallosh: Phys. Rev. D 73, 125005 (2006)
S. Ferrara, A. Strominger: in Proceedings of College Station Workshop Strings ‘89’, ed. by Arnowitt et al. (World Scienti.c, Singapore, 1989), p. 245; P. Candelas, X. de la Ossa: Nucl. Phys. B 355, 455 (1991); B. de Wit, A. Van Proeyen: Nucl. Phys. B 245, 89 (1984); E. Cremmer, C. Kounnas, A. Van Proeyen, J. P. Derendinger, S. Ferrara, B. de Wit, L. Girardello: Nucl. Phys. B 250, 385 (1985); B. de Wit, P. G. Lauwers, A. Van Proeyen: Nucl. Phys. B 255, 569 (1985); S. Ferrara, C. Kounnas, D. Lust, F. Zwirner: Nucl. Phys. B 365, 431 (1991); L. Castellani, R. D’Auria, S. Ferrara: Class. Quant. Grav. 7, 1767 (1990); L. Castellani, R. D’Auria, S. Ferrara: Phys. Lett. B 241, 57 (1990)
A. Strominger: Commun. Math. Phys. 133, 163 (1990)
L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara, P. Fré, T. Magri: J. Geom. Phys. 23, 111 (1997); L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara, P. Fré: Nucl. Phys. B 476, 397 (1996)
E. Cremmer, A. Van Proeyen: Class. Quant. Grav. 2, 445 (1985)
L. Andrianopoli, R. D’Auria, S. Ferrara, P. Fre, M. Trigiante: Nucl. Phys. B 509, 463 (1998); G. Arcioni, A. Ceresole, F. Cordaro, R. D’Auria, P. Fre, L. Gualtieri, M. Trigiante: Nucl. Phys. B 542, 273 (1999)
K. Behrndt, D. Lust, W. A. Sabra: Nucl. Phys. B 510, 264 (1998)
P. Meessen, T. Ortin: Nucl. Phys. B 749, ) 291 (2006)
P. Fré: Nucl. Phys. Proc. Suppl. 57, 52 (1997)
M. Alishahiha, H. Ebrahim: JHEP 0603, 003 (2006); M. Alishahiha, H. Ebrahim: JHEP 0611, 017 (2006)
P. Kaura, A. Misra: On the existence of non-supersymmetric black hole attractors for two-parameter Calabi-Yau’s and attractor equations, arXiv:hepth/0607132
S. Bellucci, S. Ferrara, A. Marrani, A. Yeranyan: Mirror Fermat Calabi-Yau threefolds and Landau-Ginzburg black hole attractors, arXiv:hep-th/0608091
D. Astefanesei, K. Goldstein, S. Mahapatra: Moduli and (un)attractor black hole thermodynamics, arXiv:hep-th/0611140
G. W. Gibbons, R. Kallosh, B. Kol: Phys. Rev. Lett. 77, 4992 (1996)
S. Ferrara, C. A. Savoy, B. Zumino: Phys. Lett. B 100, 393 (1981)
A. Ceresole, R. D’Auria, S. Ferrara: Nucl. Phys. Proc. Suppl. 46, 67 (1996)
R. Kallosh, B. Kol: Phys. Rev. D 53, 5344 (1996)
S. Ferrara, E. G. Gimon, R. Kallosh: Magic supergravities, N = 8 and black-hole composites, arXiv:hep-th/0606211
M. Gunaydin, O. Pavlyk: JHEP 0508, 101 (2005)
S. Bellucci, S. Ferrara, A. Marrani: Phys. Lett. B 635, 172 (2006)
S. Ferrara, M. Bodner, A. C. Cadavid: Phys. Lett. B 247, 25 (1990)
S. Bellucci, S. Ferrara, M. Gunaydin, A. Marrani: Int. J. Mod. Phys. A 21, 5043 (2006)
E. Cremmer, A. Van Proeyen: Class. Quant. Grav. 2, 445 (1985)
B. de Wit, F. Vanderseypen, A. Van Proeyen: Nucl. Phys. B 400, 463 (1993)
M. R. Douglas: JHEP 0305, 046 (2003); F. Denef, M. R. Douglas: Computational complexity of the landscape. I, arXiv:hep-th/0602072
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Andrianopoli, L., D’Auria, R., Ferrara, S., Trigiante, M. (2008). Extremal Black Holes in Supergravity. In: Gasperini, M., Maharana, J. (eds) String Theory and Fundamental Interactions. Lecture Notes in Physics, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74233-3_22
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