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Extremal tunneling and Anti-de Sitter instantons

  • Lars Aalsma
  • Jan Pieter van der Schaar
Open Access
Regular Article - Theoretical Physics
  • 47 Downloads

Abstract

We rederive and extend the amplitude for charged spherical shells tunneling through the outer horizon of charged black holes. In particular, we explicitly confirm that an effective action approach with natural initial conditions for a spherical shell, including backreaction, reduces to the tunneling integral. Consequently, we establish a universal expression for the probability of emission in terms of the change in the horizon entropy. Notably, the result for the charged black hole also captures the superradiant regime of charged particle decay at low energies. We then explore an appropriately regulated extremal and near-horizon limit, relating the tunneling amplitude to a family of gravitational instantons in the near-horizon Anti-de Sitter geometry, reducing to the known result for AdS2 domain walls to leading order in the probe limit. We comment on the relation to the Weak Gravity Conjecture and the conjectured instability of (non-supersymmetric) Anti-de Sitter vacua.

Keywords

Black Holes Black Holes in String Theory Classical Theories of Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    P. Kraus and F. Wilczek, Selfinteraction correction to black hole radiance, Nucl. Phys. B433 (1995) 403 [gr-qc/9408003] [INSPIRE].
  2. [2]
    P. Kraus and F. Wilczek, Effect of selfinteraction on charged black hole radiance, Nucl. Phys. B 437 (1995) 231 [hep-th/9411219] [INSPIRE].
  3. [3]
    M.K. Parikh and F. Wilczek, Hawking radiation as tunneling, Phys. Rev. Lett. 85 (2000) 5042 [hep-th/9907001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    S. Massar and R. Parentani, Gravitational instanton for black hole radiation, Phys. Rev. Lett. 78 (1997) 3810 [gr-qc/9701015] [INSPIRE].
  5. [5]
    J.D. Bekenstein, Statistical Black Hole Thermodynamics, Phys. Rev. D 12 (1975) 3077 [INSPIRE].
  6. [6]
    E. Keski-Vakkuri and P. Kraus, Microcanonical D-branes and back reaction, Nucl. Phys. B 491 (1997) 249 [hep-th/9610045] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The String landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
  8. [8]
    G.W. Gibbons, Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes, Commun. Math. Phys. 44 (1975) 245 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, arXiv:1610.01533 [INSPIRE].
  10. [10]
    B. Freivogel and M. Kleban, Vacua Morghulis, arXiv:1610.04564 [INSPIRE].
  11. [11]
    J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    D. Brill, Splitting of an extremal Reissner-Nordstrom throat via quantum tunneling, Phys. Rev. D 46 (1992) 1560 [hep-th/9202037] [INSPIRE].
  13. [13]
    P. Painlevé, La mécanique classique et la théorie de la relativité, C.R. Acad. Sci. (Paris) 173 (1921) 677.Google Scholar
  14. [14]
    S.W. Hawking and G.T. Horowitz, The Gravitational Hamiltonian, action, entropy and surface terms, Class. Quant. Grav. 13 (1996) 1487 [gr-qc/9501014] [INSPIRE].
  15. [15]
    S. Massar and R. Parentani, On the gravitational back reaction to Hawking radiation, gr-qc/9801043 [INSPIRE].
  16. [16]
    A. Hansen and F. Ravndal, Klein’s Paradox and Its Resolution, Phys. Scripta 23 (1981) 1036 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    R. Brito, V. Cardoso and P. Pani, Superradiance, Springer (2015).Google Scholar
  18. [18]
    J.D. Bekenstein and A. Meisels, Einstein a and B Coefficients for a Black Hole, Phys. Rev. D 15 (1977) 2775 [INSPIRE].
  19. [19]
    S.M. Carroll, M.C. Johnson and L. Randall, Extremal limits and black hole entropy, JHEP 11 (2009) 109 [arXiv:0901.0931] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B 44S10 (1966) 1 [Erratum ibid. B 48 (1967) 463] [INSPIRE].
  21. [21]
    M. Cvetič and H.H. Soleng, Supergravity domain walls, Phys. Rept. 282 (1997) 159 [hep-th/9604090] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    H. Chung, Tunneling between single- and multi-centered black hole configurations, Phys. Rev. D 86 (2012) 064036 [arXiv:1201.3028] [INSPIRE].
  23. [23]
    S. Ng and M. Perry, Brane splitting via quantum tunneling, Nucl. Phys. B 634 (2002) 209 [hep-th/0106008] [INSPIRE].
  24. [24]
    B. Pioline and J. Troost, Schwinger pair production in AdS 2, JHEP 03 (2005) 043 [hep-th/0501169] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    U.H. Danielsson, G. Dibitetto and S.C. Vargas, A swamp of non-SUSY vacua, JHEP 11 (2017) 152 [arXiv:1708.03293] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    S. Aretakis, Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I, Commun. Math. Phys. 307 (2011) 17 [arXiv:1110.2007] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    S. Aretakis, Stability and Instability of Extreme Reissner-Nordstrom Black Hole Spacetimes for Linear Scalar Perturbations II, Annales Henri Poincaré 12 (2011) 1491 [arXiv:1110.2009] [INSPIRE].
  28. [28]
    P. Zimmerman, Horizon instability of extremal Reissner-Nordström black holes to charged perturbations, Phys. Rev. D 95 (2017) 124032 [arXiv:1612.03172] [INSPIRE].
  29. [29]
    J.B. Hartle and S.W. Hawking, Path Integral Derivation of Black Hole Radiance, Phys. Rev. D 13 (1976) 2188 [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Institute for Theoretical Physics Amsterdam, Delta Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands

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