Abstract
We develop an effective theory which describes black holes with quantum mechanical horizons that is valid at scales long compared to the Schwarzschild radius but short compared to the lifetime of the black hole. Our formalism allows one to calculate the quantum mechanical effects in scattering processes involving black hole asymptotic states. We point out that the EFT Wightman functions which describe Hawking radiation in the Unruh vacuum are not Planck suppressed and are actually enhanced relative to those in the Boulware vacuum, for which such radiation is absent. We elaborate on this point showing how the non-Planck suppressed effects of Hawking radiation cancel in classical observables.
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References
S.W. Hawking, Particle creation by black holes, Commun. Math. Phys.43 (1975) 199 [Erratum ibid.46 (1976) 206] [INSPIRE].
B.S. DeWitt, Quantum theory of gravity. 1. The canonical theory, Phys. Rev.160 (1967) 1113 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Ann. Inst. H. Poincaré Phys. Theor.A 20 (1974) 69 [INSPIRE].
J.F. Donoghue, General relativity as an effective field theory: the leading quantum corrections, Phys. Rev.D 50 (1994) 3874 [gr-qc/9405057] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, An effective field theory of gravity for extended objects, Phys. Rev.D 73 (2006) 104029 [hep-th/0409156] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, Towers of gravitational theories, Gen. Rel. Grav.38 (2006) 1537 [hep-th/0605238] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, Dissipative effects in the worldline approach to black hole dynamics, Phys. Rev.D 73 (2006) 104030 [hep-th/0511133] [INSPIRE].
T. Damour, Black hole eddy currents, Phys. Rev.D 18 (1978) 3598 [INSPIRE].
R.L. Znajek, The electric and magnetic conductivity of a Kerr hole, Mon. Not. Roy. Astron. Soc.185 (1978) 833.
R.H. Price and K.S. Thorne, Membrane viewpoint on black holes: properties and evolution of the stretched horizon, Phys. Rev.D 33 (1986) 915 [INSPIRE].
P. Candelas, Vacuum polarization in Schwarzschild space-time, Phys. Rev.D 21 (1980) 2185 [INSPIRE].
J.D. Bekenstein and A. Meisels, Einstein A and B coefficients for a black hole, Phys. Rev.D 15 (1977) 2775 [INSPIRE].
P. Panangaden and R.M. Wald, Probability distribution for radiation from a black hole in the presence of incoming radiation, Phys. Rev.D 16 (1977) 929 [INSPIRE].
D.G. Boulware, Quantum field theory in Schwarzschild and Rindler spaces, Phys. Rev.D 11 (1975) 1404 [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev.D 14 (1976) 870 [INSPIRE].
J.B. Hartle and S.W. Hawking, Path integral derivation of black hole radiance, Phys. Rev.D 13 (1976) 2188 [INSPIRE].
D.N. Page, Particle emission rates from a black hole: massless particles from an uncharged, nonrotating hole, Phys. Rev.D 13 (1976) 198 [INSPIRE].
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys.2 (1961) 407 [INSPIRE].
K.T. Mahanthappa, Multiple production of photons in quantum electrodynamics, Phys. Rev.126 (1962) 329 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz.47 (1964) 1515 [Sov. Phys. JETP20 (1965) 1018] [INSPIRE].
L.K. Wong, A.-C. Davis and R. Gregory, Effective field theory for black holes with induced scalar charges, Phys. Rev.D 100 (2019) 024010 [arXiv:1903.07080] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev.140 (1965) B516 [INSPIRE].
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ArXiv ePrint: 1912.13435
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Goldberger, W.D., Rothstein, I.Z. An effective field theory of quantum mechanical black hole horizons. J. High Energ. Phys. 2020, 56 (2020). https://doi.org/10.1007/JHEP04(2020)056
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DOI: https://doi.org/10.1007/JHEP04(2020)056