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Non-supersymmetric extremal multicenter black holes with superpotentials

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Abstract

Using the superpotential approach we generalize Denef’s method of deriving and solving first-order equations describing multicenter extremal black holes in four-dimensional \( \mathcal{N} = 2 \) supergravity to allow non-supersymmetric solutions. We illustrate the general results with an explicit example of the stu model.

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References

  1. S.D. Majumdar, A class of exact solutions of Einstein’s field equations, Phys. Rev. 72 (1947) 390 [SPIRES].

    Article  ADS  Google Scholar 

  2. A. Papapetrou, A static solution of the equations of the gravitational field for an arbitrary charge distribution, Proc. Roy. Irish Acad. A 51 (1947) 191 [SPIRES].

    MathSciNet  Google Scholar 

  3. F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  4. K. Behrndt, D. Lüst and W.A. Sabra, Stationary solutions of N = 2 supergravity, Nucl. Phys. B 510 (1998) 264 [hep-th/9705169] [SPIRES].

    Article  ADS  Google Scholar 

  5. G.L. Cardoso, B. de Wit, J. Käppeli and T. Mohaupt, Stationary BPS solutions in N = 2 supergravity with R 2 interactions, JHEP 12 (2000) 019 [hep-th/0009234] [SPIRES].

    Article  Google Scholar 

  6. D. Gaiotto, W. Li and M. Padi, Non-Supersymmetric Attractor Flow in Symmetric Spaces, JHEP 12 (2007) 093 [arXiv:0710.1638] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. P. Breitenlohner, D. Maison and G.W. Gibbons, Four-Dimensional Black Holes from Kaluza-Klein Theories, Commun. Math. Phys. 120 (1988) 295 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. G. Bossard and H. Nicolai, Multi-black holes from nilpotent Lie algebra orbits, arXiv:0906.1987 [SPIRES].

  9. T. Mohaupt and K. Waite, Instantons, black holes and harmonic functions, JHEP 10 (2009) 058 [arXiv:0906.3451] [SPIRES].

    Article  Google Scholar 

  10. K. Goldstein and S. Katmadas, Almost BPS black holes, JHEP 05 (2009) 058 [arXiv:0812.4183] [SPIRES].

    Article  ADS  Google Scholar 

  11. I. Bena, S. Giusto, C. Ruef and N.P. Warner, A (Running) Bolt for New Reasons, JHEP 11 (2009) 089 [arXiv:0909.2559] [SPIRES].

    Article  Google Scholar 

  12. I. Bena, G. Dall’Agata, S. Giusto, C. Ruef and N.P. Warner, Non-BPS Black Rings and Black Holes in Taub-NUT, JHEP 06 (2009) 015 [arXiv:0902.4526] [SPIRES].

    Article  ADS  Google Scholar 

  13. I. Bena, S. Giusto, C. Ruef and N.P. Warner, Multi-Center non-BPS Black Holes - the Solution, JHEP 11 (2009) 032 [arXiv:0908.2121] [SPIRES].

    Article  Google Scholar 

  14. E.G. Gimon, F. Larsen and J. Simón, Black holes in supergravity: the non-BPS branch, JHEP 01 (2008) 040 [arXiv:0710.4967] [SPIRES].

    Article  ADS  Google Scholar 

  15. E.G. Gimon, F. Larsen and J. Simón, Constituent Model of Extremal non-BPS Black Holes, JHEP 07 (2009) 052 [arXiv:0903.0719] [SPIRES].

    Article  ADS  Google Scholar 

  16. B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, hep-th/0304094 [SPIRES].

  17. A. Ceresole and G. Dall’Agata, Flow Equations for Non-BPS Extremal Black Holes, JHEP 03 (2007) 110 [hep-th/0702088] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First Order Description of Black Holes in Moduli Space, JHEP 11 (2007) 032 [arXiv:0706.0712] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. G.L. Cardoso, A. Ceresole, G. Dall’Agata, J.M. Oberreuter and J. Perz, First-order flow equations for extremal black holes in very special geometry, JHEP 10 (2007) 063 [arXiv:0706.3373] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. J. Perz, P. Smyth, T. Van Riet and B. Vercnocke, First-order flow equations for extremal and non-extremal black holes, JHEP 03 (2009) 150 [arXiv:0810.1528] [SPIRES].

    Article  ADS  Google Scholar 

  21. L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First Order Description of D = 4 static Black Holes and the Hamilton-Jacobi equation, arXiv:0905.3938 [SPIRES].

  22. A. Ceresole, G. Dall’Agata, S. Ferrara and A. Yeranyan, First order flows for N = 2 extremal black holes and duality invariants, Nucl. Phys. B 824 (2010) 239 [arXiv:0908.1110] [SPIRES].

    Article  Google Scholar 

  23. G. Bossard, Y. Michel and B. Pioline, Extremal black holes, nilpotent orbits and the true fake superpotential, JHEP 01 (2010) 038 [arXiv:0908.1742] [SPIRES].

    Article  Google Scholar 

  24. P.K. Tripathy and S.P. Trivedi, Non-Supersymmetric Attractors in String Theory, JHEP 03 (2006) 022 [hep-th/0511117] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. R. Kallosh, N. Sivanandam and M. Soroush, Exact attractive non-BPS STU black holes, Phys. Rev. D 74 (2006) 065008 [hep-th/0606263] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  26. A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990) 163 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  27. B. Craps, F. Roose, W. Troost and A. Van Proeyen, What is special Kähler geometry?, Nucl. Phys. B 503 (1997) 565 [hep-th/9703082] [SPIRES].

    Article  ADS  Google Scholar 

  28. B. de Wit and A. Van Proeyen, Potentials and Symmetries of General Gauged N = 2 Supergravity: Yang-Mills Models, Nucl. Phys. B 245 (1984) 89 [SPIRES].

    Article  ADS  Google Scholar 

  29. B. de Wit, P.G. Lauwers and A. Van Proeyen, Lagrangians of N = 2 supergravity-matter systems, Nucl. Phys. B 255 (1985) 569 [SPIRES].

    ADS  Google Scholar 

  30. P. Candelas and X. de la Ossa, Moduli space of Calabi-Yau manifolds, Nucl. Phys. B 355 (1991) 455 [SPIRES].

    Article  ADS  Google Scholar 

  31. T.W. Grimm and J. Louis, The effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys. B 718 (2005) 153 [hep-th/0412277] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. B. Pioline, Lectures on black holes, topological strings and quantum attractors (2.0), Lect. Notes Phys. 755 (2008) 283 [hep-th/0607227] [SPIRES].

    MathSciNet  Google Scholar 

  33. F. Denef, B.R. Greene and M. Raugas, Split attractor flows and the spectrum of BPS D-branes on the quintic, JHEP 05 (2001) 012 [hep-th/0101135] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  34. J. de Boer, F. Denef, S. El-Showk, I. Messamah and D. Van den Bleeken, Black hole bound states in AdS 3 × S 2, JHEP 11 (2008) 050 [arXiv:0802.2257] [SPIRES].

    Article  Google Scholar 

  35. W. Van Herck and T. Wyder, Black Hole Meiosis, arXiv:0909.0508 [SPIRES].

  36. M. Bodner, A.C. Cadavid and S. Ferrara, (2, 2) vacuum configurations for type IIA superstrings: N = 2 supergravity Lagrangians and algebraic geometry, Class. Quant. Grav. 8 (1991) 789 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  37. S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  39. S. Bellucci, A. Marrani, E. Orazi and A. Shcherbakov, Attractors with Vanishing Central Charge, Phys. Lett. B 655 (2007) 185 [arXiv:0707.2730] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  40. A. Van Proeyen and B. Vercnocke, Effective action for the field equations of charged black holes, Class. Quant. Grav. 25 (2008) 035010 [arXiv:0708.2829] [SPIRES].

    Article  ADS  Google Scholar 

  41. C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation, Freeman, San Francisco U.S.A. (1973).

    Google Scholar 

  42. J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, Quantizing N = 2 Multicenter Solutions, JHEP 05 (2009) 002 [arXiv:0807.4556] [SPIRES].

    Article  Google Scholar 

  43. S. Bellucci, S. Ferrara, A. Marrani and A. Yeranyan, stu black holes unveiled, arXiv:0807.3503 [SPIRES].

  44. C. Stelea, K. Schleich and D. Witt, Charged Kaluza-Klein multi-black holes in five dimensions, arXiv:0909.3835 [SPIRES].

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Authors and Affiliations

  1. Dipartimento di Fisica, Sezione Teorica, Università degli Studi di Milano, via Celoria 16, 20133, Milano, Italy

    Pietro Galli

  2. Afdeling Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D bus 2415, 3001, Heverlee, Belgium

    Jan Perz

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  1. Pietro Galli
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  2. Jan Perz
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Correspondence to Pietro Galli.

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ArXiv ePrint: 0909.5185

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Galli, P., Perz, J. Non-supersymmetric extremal multicenter black holes with superpotentials. J. High Energ. Phys. 2010, 102 (2010). https://doi.org/10.1007/JHEP02(2010)102

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  • DOI: https://doi.org/10.1007/JHEP02(2010)102

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