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Separability of black holes in string theory

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Abstract

We analyze the origin of separability for rotating black holes in string theory, considering both massless and massive geodesic equations as well as the corresponding wave equations. We construct a conformal Killing-Stackel tensor for a general class of black holes with four independent charges, then identify two-charge configurations where enhancement to an exact Killing-Stackel tensor is possible. We show that further enhancement to a conserved Killing-Yano tensor is possible only for the special case of Kerr-Newman black holes. We construct natural null congruences for all these black holes and use the results to show that only the Kerr-Newman black holes are algebraically special in the sense of Petrov. Modifying the asymptotic behavior by the subtraction procedure that induces an exact SL(2)2 also preserves only the conformal Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black hole possesses a conformal Killing-Stackel tensor but has no further enhancements.

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References

  1. R.P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11 (1963) 237 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. E.T. Newman et al., Metric of a rotating, charged mass, J. Math. Phys. 6 (1965) 918 [INSPIRE].

    Article  ADS  Google Scholar 

  3. B. Carter, Hamilton-Jacobi and Schrödinger separable solutions of Einstein’s equations, Commun. Math. Phys. 10 (1968) 280 [INSPIRE].

    MATH  Google Scholar 

  4. B. Carter, Global structure of the Kerr family of gravitational fields, Phys. Rev. 174 (1968) 1559 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  5. B. Carter, Republication of “Black hole equilibrium states. Part 1: analytic and geometric properties of the Kerr solutions”, Gen. Rel. Grav. 41 (2009) 2873.

    Article  ADS  MATH  Google Scholar 

  6. B. Carter, Killing tensor quantum numbers and conserved currents in curved space, Phys. Rev. D 16 (1977) 3395 [INSPIRE].

    ADS  Google Scholar 

  7. H. Stephani, A note on Killing tensors, Gen. Rel. Grav. 9 (1978) 789 .

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. S. Benenti and M. Francaviglia, Remarks on certain separability structures and their applications to general relativity 1, Gen. Rel. Grav. 10 (1979) 79.

    Article  ADS  MATH  Google Scholar 

  9. H. Stephani et al., Exact solutions of Einstein’s field equations, Cambridge University Press, Cambridge U.K. (2003).

    Book  MATH  Google Scholar 

  10. V.P. Frolov and D. Kubiznak, Higher-dimensional black holes: hidden symmetries and separation of variables, Class. Quant. Grav. 25 (2008) 154005 [arXiv:0802.0322] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. D. Kubiznak, Black hole spacetimes with Killing-Yano symmetries, arXiv:0909.1589 [INSPIRE].

  12. M. Cariglia, P. Krtous and D. Kubiznak, Hidden symmetries and integrability in higher dimensional rotating black hole spacetimes, Fortsch. Phys. 60 (2012) 947 [arXiv:1112.5446] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  13. J.M. Maldacena and A. Strominger, Universal low-energy dynamics for rotating black holes, Phys. Rev. D 56 (1997) 4975 [hep-th/9702015] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. M. Cvetič and F. Larsen, General rotating black holes in string theory: grey body factors and event horizons, Phys. Rev. D 56 (1997) 4994 [hep-th/9705192] [INSPIRE].

    ADS  Google Scholar 

  15. M. Cvetič and F. Larsen, Grey body factors for rotating black holes in four-dimensions, Nucl. Phys. B 506 (1997) 107 [hep-th/9706071] [INSPIRE].

    Article  ADS  Google Scholar 

  16. D.D. Chow, Symmetries of supergravity black holes, Class. Quant. Grav. 27 (2010) 205009 [arXiv:0811.1264] [INSPIRE].

    Article  ADS  Google Scholar 

  17. F. Larsen, A string model of black hole microstates, Phys. Rev. D 56 (1997) 1005 [hep-th/9702153] [INSPIRE].

    ADS  Google Scholar 

  18. A. Castro, A. Maloney and A. Strominger, Hidden conformal symmetry of the Kerr black hole, Phys. Rev. D 82 (2010) 024008 [arXiv:1004.0996] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  19. M. Cvetič and F. Larsen, Conformal symmetry for general black holes, JHEP 02 (2012) 122 [arXiv:1106.3341] [INSPIRE].

    Article  ADS  Google Scholar 

  20. M. Cvetič and F. Larsen, Conformal symmetry for black holes in four dimensions, JHEP 09 (2012) 076 [arXiv:1112.4846] [INSPIRE].

    Article  ADS  Google Scholar 

  21. B. Carter and R. Mclenaghan, Generalized total angular momentum operator for the Dirac equation in curved space-time, Phys. Rev. D 19 (1979) 1093 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  22. G. Gibbons, R. Rietdijk and J. van Holten, SUSY in the sky, Nucl. Phys. B 404 (1993) 42 [hep-th/9303112] [INSPIRE].

    Article  ADS  Google Scholar 

  23. F. De Jonghe, K. Peeters and K. Sfetsos, Killing-Yano supersymmetry in string theory, Class. Quant. Grav. 14 (1997) 35 [hep-th/9607203] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  24. D. Kubiznak, H.K. Kunduri and Y. Yasui, Generalized Killing-Yano equations in D = 5 gauged supergravity, Phys. Lett. B 678 (2009) 240 [arXiv:0905.0722] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  25. F. Larsen, Rotating Kaluza-Klein black holes, Nucl. Phys. B 575 (2000) 211 [hep-th/9909102] [INSPIRE].

    Article  ADS  Google Scholar 

  26. G.T. Horowitz, T. Wiseman and T. Wiseman, General black holes in Kaluza-Klein theory, arXiv:1107.5563 [INSPIRE].

  27. M. Cvetič and D. Youm, General rotating five-dimensional black holes of toroidally compactified heterotic string, Nucl. Phys. B 476 (1996) 118 [hep-th/9603100] [INSPIRE].

    Article  ADS  Google Scholar 

  28. M. Cvetič and D. Youm, All the static spherically symmetric black holes of heterotic string on a six torus, Nucl. Phys. B 472 (1996) 249 [hep-th/9512127] [INSPIRE].

    Article  ADS  Google Scholar 

  29. M. Cvetič and C.M. Hull, Black holes and U duality, Nucl. Phys. B 480 (1996) 296 [hep-th/9606193] [INSPIRE].

    Article  ADS  Google Scholar 

  30. M. Demianski and M. Francaviglia, Separability structures and Killing-Yano tensors in vacuum type-D space-times without acceleration, Int. J. Theor. Phys. 19 (1980) 675.

    Article  MathSciNet  MATH  Google Scholar 

  31. S. Benenti, Intrinsic characterization of the variable separation in the Hamilton-Jacobi equation, J. Math. Phys. 38 (1997) 6578.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. P. Davis, Separability of multi-charge black holes in supergravity, Class. Quant. Grav. 23 (2006) 6829 [hep-th/0607065] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  33. L. Mariot, Le champ électromagnétique singulier, CR. Acad. Sci. Paris (1954) 1189.

  34. I. Robinson, Null electromagnetic fields, J. Math. Phys. 2 (1961) 290

    Article  ADS  Google Scholar 

  35. I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Cargese lectures on the Kerr/CFT correspondence, Nucl. Phys. Proc. Suppl. 216 (2011) 194 [arXiv:1103.2355] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. P. Taxiarchis, Space-times admitting Penrose-Floyd tensors, Gen. Rel. Grav. 17 (1985) 2.

    Article  MathSciNet  Google Scholar 

  37. E. Glass and J.M. Kress, Solutions of Penrose’s equation, J. Math. Phys. 40 (1999) 309 [gr-qc/9809074] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. L. Mason and A. Taghavi-Chabert, Killing-Yano tensors and multi-hermitian structures, J. Geom. Phys. 60 (2010) 907.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. S.-Q. Wu, Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory, Phys. Rev. D 80 (2009) 044037 [Erratum ibid. D 80 (2009) 069902] [arXiv:0902.2823] [INSPIRE].

    ADS  Google Scholar 

  40. T. Houri, D. Kubiznak, C.M. Warnick and Y. Yasui, Local metrics admitting a principal Killing-Yano tensor with torsion, Class. Quant. Grav. 29 (2012) 165001 [arXiv:1203.0393] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Michigan, Ann Arbor, MI, 48109, U.S.A.

    Cynthia Keeler & Finn Larsen

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  1. Cynthia Keeler
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  2. Finn Larsen
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Correspondence to Cynthia Keeler.

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ArXiv ePrint: 1207.5928

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Keeler, C., Larsen, F. Separability of black holes in string theory. J. High Energ. Phys. 2012, 152 (2012). https://doi.org/10.1007/JHEP10(2012)152

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