Hawking radiation in a Plebanski-Demianski black hole

Article
First Online:
Received:
Accepted:

Abstract

In this paper, we show the flux of Hawking radiation in a Plebanski-Demianski black hole from the point of view of gauge and gravitational anomalies. We will use the consistent anomaly method to guarantee that our results are valid in the de Sitter space. This is because we are including the cosmological constant into our parameters and the covariant anomaly method gives a wrong value for the Hawking temperature. We also show that these calculations are a general result. In order to verify the consistence of our results, we can reproduce earlier known results as certain limiting cases.

Keywords

Black Holes Anomalies in Field and String Theories Spacetime Singularities Space-Time Symmetries 
This is a preview of subscription content, log in to check access.

References

  1. [1]
    Y.B. Zeldovich and A.A. Starobinsky, Particle production and vacuum polarization in an anisotropic gravitational field, Zh. Eksp. Teor. Fiz. 61 (1971) 2161 [Sov. Phys. JETP 34 (1972) 1159] [INSPIRE].ADSGoogle Scholar
  2. [2]
    S.W. Hawking, Black hole explosions?, Nature 248 (1974) 30 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    S.W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    G. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].MathSciNetADSGoogle Scholar
  5. [5]
    G. Gibbons and S.W. Hawking, Cosmological event horizons, thermodynamics and particle creation, Phys. Rev. D 15 (1977) 2738 [INSPIRE].MathSciNetADSGoogle Scholar
  6. [6]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].MathSciNetADSGoogle Scholar
  7. [7]
    A.W. Peet, TASI lectures on black holes in string theory, hep-th/0008241 [INSPIRE].
  8. [8]
    S.M. Christensen and S.A. Fulling, Trace anomalies and the Hawking effect, Phys. Rev. D 15 (1977) 2088 [INSPIRE].ADSGoogle Scholar
  9. [9]
    S.P. Robinson and F. Wilczek, A relationship between Hawking radiation and gravitational anomalies, Phys. Rev. Lett. 95 (2005) 011303 [gr-qc/0502074] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    S. Iso, H. Umetsu and F. Wilczek, Hawking radiation from charged black holes via gauge and gravitational anomalies, Phys. Rev. Lett. 96 (2006) 151302 [hep-th/0602146] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    S. Iso, H. Umetsu and F. Wilczek, Anomalies, Hawking radiations and regularity in rotating black holes, Phys. Rev. D 74 (2006) 044017 [hep-th/0606018] [INSPIRE].MathSciNetADSGoogle Scholar
  12. [12]
    K. Murata and J. Soda, Hawking radiation from rotating black holes and gravitational anomalies, Phys. Rev. D 74 (2006) 044018 [hep-th/0606069] [INSPIRE].MathSciNetADSGoogle Scholar
  13. [13]
    Z. Xu and B. Chen, Hawking radiation from general Kerr-(anti)de Sitter black holes, Phys. Rev. D 75 (2007) 024041 [hep-th/0612261] [INSPIRE].ADSGoogle Scholar
  14. [14]
    Q.-Q. Jiang and S.-Q. Wu, Hawking radiation from rotating black holes in anti-de Sitter spaces via gauge and gravitational anomalies, Phys. Lett. B 647 (2007) 200 [hep-th/0701002] [INSPIRE].MathSciNetADSGoogle Scholar
  15. [15]
    S. Iso, T. Morita and H. Umetsu, Quantum anomalies at horizon and Hawking radiations in Myers-Perry black holes, JHEP 04 (2007) 068 [hep-th/0612286] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    K. Lin, S.W. Chen and S.Z. Yang, Anomalies and Hawking radiation of NUT-Kerr-Newman de Sitter black hole, Int. J. Theor. Phys. 47 (2008) 2453 [INSPIRE].MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    J.F. Plebanski and M. Demianski, Rotating, charged and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  18. [18]
    S. Iso, T. Morita and H. Umetsu, Higher-spin currents and thermal flux from Hawking radiation, Phys. Rev. D 75 (2007) 124004 [hep-th/0701272] [INSPIRE].MathSciNetADSGoogle Scholar
  19. [19]
    S. Iso, T. Morita and H. Umetsu, Fluxes of higher-spin currents and Hawking radiations from charged black holes, Phys. Rev. D 76 (2007) 064015 [arXiv:0705.3494] [INSPIRE].MathSciNetADSGoogle Scholar
  20. [20]
    S. Iso, T. Morita and H. Umetsu, Higher-spin gauge and trace anomalies in two-dimensional backgrounds, Nucl. Phys. B 799 (2008) 60 [arXiv:0710.0453] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    S. Iso, T. Morita and H. Umetsu, Hawking radiation via higher-spin gauge anomalies, Phys. Rev. D 77 (2008) 045007 [arXiv:0710.0456] [INSPIRE].MathSciNetADSGoogle Scholar
  22. [22]
    L. Bonora and M. Cvitan, Hawking radiation, W ∞ algebra and trace anomalies, JHEP 05 (2008) 071 [arXiv:0804.0198] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    L. Bonora, M. Cvitan, S. Pallua and I. Smolić, Hawking fluxes, W ∞ algebra and anomalies, JHEP 12 (2008) 021 [arXiv:0808.2360] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    L. Bonora, M. Cvitan, S. Pallua and I. Smolić, Hawking fluxes, fermionic currents, W 1+∞ algebra and anomalies, Phys. Rev. D 80 (2009) 084034 [arXiv:0907.3722] [INSPIRE].ADSGoogle Scholar
  25. [25]
    E.C. Vagenas and S. Das, Gravitational anomalies, Hawking radiation and spherically symmetric black holes, JHEP 10 (2006) 025 [hep-th/0606077] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    S. Das, S.P. Robinson and E.C. Vagenas, Gravitational anomalies: a recipe for Hawking radiation, Int. J. Mod. Phys. D 17 (2008) 533 [arXiv:0705.2233] [INSPIRE].MathSciNetADSGoogle Scholar
  27. [27]
    V. Akhmedova, T. Pilling, A. de Gill and D. Singleton, Comments on anomaly versus WKB/tunneling methods for calculating Unruh radiation, Phys. Lett. B 673 (2009) 227 [arXiv:0808.3413] [INSPIRE].ADSGoogle Scholar
  28. [28]
    A. Zampeli, D. Singleton and E.C. Vagenas, Hawking radiation, chirality and the principle of effective theory of gravity, JHEP 06 (2012) 097 [arXiv:1206.0879] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    Q.-Q. Jiang, Hawking radiation from black holes in de Sitter spaces, Class. Quant. Grav. 24 (2007) 4391 [arXiv:0705.2068] [INSPIRE].ADSMATHCrossRefGoogle Scholar
  30. [30]
    J.B. Griffiths and J. Podolský, A new look at the Plebanski-Demianski family of solutions, Int. J. Mod. Phys. D 15 (2006) 335 [gr-qc/0511091] [INSPIRE].ADSGoogle Scholar
  31. [31]
    D. Zwanziger, Local Lagrangian quantum field theory of electric and magnetic charges, Phys. Rev. D 3 (1971) 880 [INSPIRE].MathSciNetADSGoogle Scholar
  32. [32]
    D. Singleton, Magnetic charge as a “hidden” gauge symmetry, Int. J. Theor. Phys. 34 (1995) 37 [hep-th/9701044] [INSPIRE].MathSciNetMATHCrossRefGoogle Scholar
  33. [33]
    R.A. Bertlmann, Anomalies in quantum field theory, Oxford University Press, Oxford U.K. (1996) [INSPIRE].MATHGoogle Scholar
  34. [34]
    A. Bilal, Lectures on anomalies, arXiv:0802.0634 [INSPIRE].
  35. [35]
    L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    R.A. Bertlmann and E. Kohlprath, Two-dimensional gravitational anomalies, Schwinger terms and dispersion relations, Annals Phys. 288 (2001) 137 [hep-th/0011067] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Rudjer Bošković InstituteZagrebCroatia

Personalised recommendations