Abstract
We provide a method to calculate the rate of false vacuum decay induced by a black hole. The method uses complex tunneling solutions and consistently takes into account the structure of different quantum vacua in the black hole metric via boundary conditions. The latter are connected to the asymptotic behavior of the time-ordered Green’s function in the corresponding vacua. We illustrate the technique on a two-dimensional toy model of a scalar field with inverted Liouville potential in an external background of a dilaton black hole. We analytically derive the exponential suppression of tunneling from the Boulware, Hartle-Hawking and Unruh vacua and show that they are parametrically different. The Unruh vacuum decay rate is exponentially smaller than the decay rate of the Hartle-Hawking state, though both rates become unsuppressed at high enough black hole temperature. We interpret the vanishing suppression of the Unruh vacuum decay at high temperature as an artifact of the two-dimensional model and discuss why this result can be modified in the realistic case of black holes in four dimensions.
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References
W.A. Hiscock, Can black holes nucleate vacuum phase transitions?, Phys. Rev. D 35 (1987) 1161 [INSPIRE].
V.A. Berezin, V.A. Kuzmin and I.I. Tkachev, O(3) Invariant Tunneling in General Relativity, Phys. Lett. B 207 (1988) 397 [INSPIRE].
P.B. Arnold, Gravity and false vacuum decay rates: O(3) solutions, Nucl. Phys. B 346 (1990) 160 [INSPIRE].
V.A. Berezin, V.A. Kuzmin and I.I. Tkachev, Black holes initiate false vacuum decay, Phys. Rev. D 43 (1991) 3112 [INSPIRE].
R.A. Flores and M. Sher, Upper Limits to Fermion Masses in the Glashow-Weinberg-Salam Model, Phys. Rev. D 27 (1983) 1679 [INSPIRE].
M. Sher, Electroweak Higgs Potentials and Vacuum Stability, Phys. Rept. 179 (1989) 273 [INSPIRE].
G. Isidori, G. Ridolfi and A. Strumia, On the metastability of the standard model vacuum, Nucl. Phys. B 609 (2001) 387 [hep-ph/0104016] [INSPIRE].
F. Bezrukov, M.Y. Kalmykov, B.A. Kniehl and M. Shaposhnikov, Higgs Boson Mass and New Physics, JHEP 10 (2012) 140 [arXiv:1205.2893] [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].
A.V. Bednyakov, B.A. Kniehl, A.F. Pikelner and O.L. Veretin, Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision, Phys. Rev. Lett. 115 (2015) 201802 [arXiv:1507.08833] [INSPIRE].
A. Andreassen, W. Frost and M.D. Schwartz, Scale Invariant Instantons and the Complete Lifetime of the Standard Model, Phys. Rev. D 97 (2018) 056006 [arXiv:1707.08124] [INSPIRE].
R. Gregory, I.G. Moss and B. Withers, Black holes as bubble nucleation sites, JHEP 03 (2014) 081 [arXiv:1401.0017] [INSPIRE].
P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [arXiv:1501.04937] [INSPIRE].
P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [arXiv:1503.07331] [INSPIRE].
P. Burda, R. Gregory and I. Moss, The fate of the Higgs vacuum, JHEP 06 (2016) 025 [arXiv:1601.02152] [INSPIRE].
J. García-Bellido, A.D. Linde and D. Wands, Density perturbations and black hole formation in hybrid inflation, Phys. Rev. D 54 (1996) 6040 [astro-ph/9605094] [INSPIRE].
T. Fujita, M. Kawasaki, K. Harigaya and R. Matsuda, Baryon asymmetry, dark matter, and density perturbation from primordial black holes, Phys. Rev. D 89 (2014) 103501 [arXiv:1401.1909] [INSPIRE].
R. Allahverdi, J. Dent and J. Osinski, Nonthermal production of dark matter from primordial black holes, Phys. Rev. D 97 (2018) 055013 [arXiv:1711.10511] [INSPIRE].
O. Lennon, J. March-Russell, R. Petrossian-Byrne and H. Tillim, Black Hole Genesis of Dark Matter, JCAP 04 (2018) 009 [arXiv:1712.07664] [INSPIRE].
L. Morrison, S. Profumo and Y. Yu, Melanopogenesis: Dark Matter of (almost) any Mass and Baryonic Matter from the Evaporation of Primordial Black Holes weighing a Ton (or less), JCAP 05 (2019) 005 [arXiv:1812.10606] [INSPIRE].
D. Hooper, G. Krnjaic and S.D. McDermott, Dark Radiation and Superheavy Dark Matter from Black Hole Domination, JHEP 08 (2019) 001 [arXiv:1905.01301] [INSPIRE].
D. Hooper, G. Krnjaic, J. March-Russell, S.D. McDermott and R. Petrossian-Byrne, Hot Gravitons and Gravitational Waves From Kerr Black Holes in the Early Universe, arXiv:2004.00618 [INSPIRE].
V. De Luca, G. Franciolini, A. Kehagias and A. Riotto, Standard model baryon number violation seeded by black holes, Phys. Lett. B 819 (2021) 136454 [arXiv:2102.07408] [INSPIRE].
B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, Constraints on Primordial Black Holes, arXiv:2002.12778 [INSPIRE].
F.R. Klinkhamer and N.S. Manton, A Saddle Point Solution in the Weinberg-Salam Theory, Phys. Rev. D 30 (1984) 2212 [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].
N. Tetradis, Black holes and Higgs stability, JCAP 09 (2016) 036 [arXiv:1606.04018] [INSPIRE].
D. Gorbunov, D. Levkov and A. Panin, Fatal youth of the Universe: black hole threat for the electroweak vacuum during preheating, JCAP 10 (2017) 016 [arXiv:1704.05399] [INSPIRE].
K. Mukaida and M. Yamada, False Vacuum Decay Catalyzed by Black Holes, Phys. Rev. D 96 (2017) 103514 [arXiv:1706.04523] [INSPIRE].
K. Kohri and H. Matsui, Electroweak Vacuum Collapse induced by Vacuum Fluctuations of the Higgs Field around Evaporating Black Holes, Phys. Rev. D 98 (2018) 123509 [arXiv:1708.02138] [INSPIRE].
T. Hayashi, K. Kamada, N. Oshita and J. Yokoyama, On catalyzed vacuum decay around a radiating black hole and the crisis of the electroweak vacuum, JHEP 08 (2020) 088 [arXiv:2005.12808] [INSPIRE].
D. Canko, I. Gialamas, G. Jelic-Cizmek, A. Riotto and N. Tetradis, On the Catalysis of the Electroweak Vacuum Decay by Black Holes at High Temperature, Eur. Phys. J. C 78 (2018) 328 [arXiv:1706.01364] [INSPIRE].
D.-C. Dai, R. Gregory and D. Stojkovic, Connecting the Higgs Potential and Primordial Black Holes, Phys. Rev. D 101 (2020) 125012 [arXiv:1909.00773] [INSPIRE].
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
S.W. Hawking and I.G. Moss, Supercooled Phase Transitions in the Very Early Universe, Phys. Lett. B 110 (1982) 35 [INSPIRE].
S. Tomsovic, Tunneling in Complex Systems, World scientific (1998) [DOI].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE].
C.G. Callan Jr. and S.R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev. D 16 (1977) 1762 [INSPIRE].
S.R. Coleman, The Uses of Instantons, Subnucl. Ser. 15 (1979) 805 [INSPIRE].
W.H. Miller, Classical-limit quantum mechanics and the theory of molecular collisions, in Advances in Chemical Physics, pp. 69–177, John Wiley & Sons, Ltd (1974) [DOI].
V.A. Rubakov, D.T. Son and P.G. Tinyakov, Classical boundary value problem for instanton transitions at high-energies, Phys. Lett. B 287 (1992) 342 [INSPIRE].
G.F. Bonini, A.G. Cohen, C. Rebbi and V.A. Rubakov, The Semiclassical description of tunneling in scattering with multiple degrees of freedom, Phys. Rev. D 60 (1999) 076004 [hep-ph/9901226] [INSPIRE].
F.L. Bezrukov and D. Levkov, Dynamical tunneling of bound systems through a potential barrier: complex way to the top, J. Exp. Theor. Phys. 98 (2004) 820 [quant-ph/0312144] [INSPIRE].
S.F. Bramberger, G. Lavrelashvili and J.-L. Lehners, Quantum tunneling from paths in complex time, Phys. Rev. D 94 (2016) 064032 [arXiv:1605.02751] [INSPIRE].
N. Turok, On Quantum Tunneling in Real Time, New J. Phys. 16 (2014) 063006 [arXiv:1312.1772] [INSPIRE].
A. Cherman and M. Ünsal, Real-Time Feynman Path Integral Realization of Instantons, arXiv:1408.0012 [INSPIRE].
A. Andreassen, D. Farhi, W. Frost and M.D. Schwartz, Direct Approach to Quantum Tunneling, Phys. Rev. Lett. 117 (2016) 231601 [arXiv:1602.01102] [INSPIRE].
A. Andreassen, D. Farhi, W. Frost and M.D. Schwartz, Precision decay rate calculations in quantum field theory, Phys. Rev. D 95 (2017) 085011 [arXiv:1604.06090] [INSPIRE].
F.L. Bezrukov, D. Levkov, C. Rebbi, V.A. Rubakov and P. Tinyakov, Semiclassical study of baryon and lepton number violation in high-energy electroweak collisions, Phys. Rev. D 68 (2003) 036005 [hep-ph/0304180] [INSPIRE].
V.A. Rubakov and S.M. Sibiryakov, False vacuum decay in de Sitter space-time, Theor. Math. Phys. 120 (1999) 1194 [gr-qc/9905093] [INSPIRE].
A.N. Kuznetsov and P.G. Tinyakov, False vacuum decay induced by particle collisions, Phys. Rev. D 56 (1997) 1156 [hep-ph/9703256] [INSPIRE].
D. Levkov and S. Sibiryakov, Real-time instantons and suppression of collision-induced tunneling, JETP Lett. 81 (2005) 53 [hep-th/0412253] [INSPIRE].
S. Demidov and D. Levkov, High-energy limit of collision-induced false vacuum decay, JHEP 06 (2015) 123 [arXiv:1503.06339] [INSPIRE].
D.G. Levkov and S.M. Sibiryakov, Induced tunneling in QFT: Soliton creation in collisions of highly energetic particles, Phys. Rev. D 71 (2005) 025001 [hep-th/0410198] [INSPIRE].
S.V. Demidov and D.G. Levkov, Soliton-antisoliton pair production in particle collisions, Phys. Rev. Lett. 107 (2011) 071601 [arXiv:1103.0013] [INSPIRE].
S.V. Demidov and D.G. Levkov, Semiclassical description of soliton-antisoliton pair production in particle collisions, JHEP 11 (2015) 066 [arXiv:1509.07125] [INSPIRE].
F. Bezrukov, D. Levkov and S. Sibiryakov, Semiclassical S-matrix for black holes, JHEP 12 (2015) 002 [arXiv:1503.07181] [INSPIRE].
M. Fitkevich, D. Levkov and S. Sibiryakov, Semiclassical S -matrix and black hole entropy in dilaton gravity, JHEP 08 (2020) 142 [arXiv:2006.03606] [INSPIRE].
D.G. Levkov, A.G. Panin and S.M. Sibiryakov, Complex trajectories in chaotic dynamical tunneling, Phys. Rev. E 76 (2007) 046209 [nlin/0701063].
D.G. Levkov, A.G. Panin and S.M. Sibiryakov, On the over-barrier reflection in quantum mechanics with multiple degrees of freedom, Phys. Rev. A 76 (2007) 032114 [arXiv:0704.0409] [INSPIRE].
D.G. Levkov, A.G. Panin and S.M. Sibiryakov, Unstable Semiclassical Trajectories in Tunneling, Phys. Rev. Lett. 99 (2007) 170407 [arXiv:0707.0433] [INSPIRE].
D.G. Levkov, A.G. Panin and S.M. Sibiryakov, Signatures of unstable semiclassical trajectories in tunneling, J. Phys. A 42 (2009) 205102 [arXiv:0811.3391] [INSPIRE].
T. Miyachi and J. Soda, False vacuum decay in a two-dimensional black hole spacetime, Phys. Rev. D 103 (2021) 085009 [arXiv:2102.02462] [INSPIRE].
W.-Y. Ai, Correspondence between Thermal and Quantum Vacuum Transitions around Horizons, JHEP 03 (2019) 164 [arXiv:1812.06962] [INSPIRE].
D.G. Boulware, Quantum Field Theory in Schwarzschild and Rindler Spaces, Phys. Rev. D 11 (1975) 1404 [INSPIRE].
N.D. Birrell and P.C.W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, U.K. (1984) [DOI] [INSPIRE].
K. Takahashi and K.S. Ikeda, Complex-classical mechanism of the tunnelling process in strongly coupled 1.5-dimensional barrier systems, J. Phys. A 36 (2003) 7953.
K. Takahashi and K.S. Ikeda, An intrinsic multi-dimensional mechanism of barrier tunneling, Europhys. Lett. 71 (2005) 193.
S.R. Coleman, V. Glaser and A. Martin, Action Minima Among Solutions to a Class of Euclidean Scalar Field Equations, Commun. Math. Phys. 58 (1978) 211 [INSPIRE].
K. Blum, M. Honda, R. Sato, M. Takimoto and K. Tobioka, O(N ) Invariance of the Multi-Field Bounce, JHEP 05 (2017) 109 [Erratum ibid. 06 (2017) 060] [arXiv:1611.04570] [INSPIRE].
J. Byeon, L. Jeanjean and M. Mariş, Symmetry and monotonicity of least energy solutions, arXiv:0806.0299.
A.D. Linde, Decay of the False Vacuum at Finite Temperature, Nucl. Phys. B 216 (1983) 421 [Erratum ibid. 223 (1983) 544] [INSPIRE].
D.Y. Grigoriev and V.A. Rubakov, Soliton Pair Creation at Finite Temperatures. Numerical Study in (1 + 1)-dimensions, Nucl. Phys. B 299 (1988) 67 [INSPIRE].
D.Y. Grigoriev, V.A. Rubakov and M.E. Shaposhnikov, Sphaleron Transitions at Finite Temperatures: Numerical Study in (1 + 1)-dimensions, Phys. Lett. B 216 (1989) 172 [INSPIRE].
D.Y. Grigoriev, V.A. Rubakov and M.E. Shaposhnikov, Topological transitions at finite temperatures: a real time numerical approach, Nucl. Phys. B 326 (1989) 737 [INSPIRE].
S. Khlebnikov, L. Kofman, A.D. Linde and I. Tkachev, First order nonthermal phase transition after preheating, Phys. Rev. Lett. 81 (1998) 2012 [hep-ph/9804425] [INSPIRE].
I. Affleck, On Constrained Instantons, Nucl. Phys. B 191 (1981) 429 [INSPIRE].
J. Braden, M.C. Johnson, H.V. Peiris, A. Pontzen and S. Weinfurtner, New Semiclassical Picture of Vacuum Decay, Phys. Rev. Lett. 123 (2019) 031601 [arXiv:1806.06069] [INSPIRE].
M.P. Hertzberg and M. Yamada, Vacuum Decay in Real Time and Imaginary Time Formalisms, Phys. Rev. D 100 (2019) 016011 [arXiv:1904.08565] [INSPIRE].
M.P. Hertzberg, F. Rompineve and N. Shah, Quantitative Analysis of the Stochastic Approach to Quantum Tunneling, Phys. Rev. D 102 (2020) 076003 [arXiv:2009.00017] [INSPIRE].
C.G. Callan Jr., S.B. Giddings, J.A. Harvey and A. Strominger, Evanescent black holes, Phys. Rev. D 45 (1992) R1005 [hep-th/9111056] [INSPIRE].
N. Oshita, M. Yamada and M. Yamaguchi, Compact objects as the catalysts for vacuum decays, Phys. Lett. B 791 (2019) 149 [arXiv:1808.01382] [INSPIRE].
V. Cardoso and P. Pani, Testing the nature of dark compact objects: a status report, Living Rev. Rel. 22 (2019) 4 [arXiv:1904.05363] [INSPIRE].
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Shkerin, A., Sibiryakov, S. Black hole induced false vacuum decay from first principles. J. High Energ. Phys. 2021, 197 (2021). https://doi.org/10.1007/JHEP11(2021)197
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DOI: https://doi.org/10.1007/JHEP11(2021)197