Abstract
Recently, there are comparable revised interests in bubble nucleation seeded by black holes. However, it is debated in the literature that whether one shall interpret a static bounce solution in the Euclidean Schwarzschild spacetime (with periodic Euclidean Schwarzschild time) as describing a false vacuum decay at zero temperature or at finite temperature. In this paper, we show a correspondence that the static bounce solution describes either a thermal transition of vacuum in the static region outside of a Schwarzschild black hole or a quantum transition in a maximally extended Kruskal-Szekeres spacetime, corresponding to the viewpoint of the external static observers or the freely falling observers, respectively. The Matsubara modes in the thermal interpretation can be mapped to the circular harmonic modes from an O(2) symmetry in the tunneling interpretation. The complementary tunneling interpretation must be given in the Kruskal-Szekeres spacetime because of the so-called thermofield dynamics. This correspondence is general for bubble nucleation around horizons. We propose a new paradox from black holes as a consequence of this correspondence.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [INSPIRE].
L. Susskind, L. Thorlacius and J. Uglum, The Stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
L. Susskind and L. Thorlacius, Gedanken experiments involving black holes, Phys. Rev. D 49 (1994) 966 [hep-th/9308100] [INSPIRE].
A.R. Brown and E.J. Weinberg, Thermal derivation of the Coleman-De Luccia tunneling prescription, Phys. Rev. D 76 (2007) 064003 [arXiv:0706.1573] [INSPIRE].
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [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].
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].
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].
K. Mukaida and M. Yamada, False Vacuum Decay Catalyzed by Black Holes, Phys. Rev. D 96 (2017) 103514 [arXiv:1706.04523] [INSPIRE].
R. Gregory, K.M. Marshall, F. Michel and I.G. Moss, Negative modes of Coleman-De Luccia and black hole bubbles, Phys. Rev. D 98 (2018) 085017 [arXiv:1808.02305] [INSPIRE].
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
CDF and D0 collaborations and Tevatron Electroweak Working Group, Combination of CDF and D0 results on the mass of the top quark using up to 5.8 fb −1 of data, arXiv:1107.5255 [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].
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].
S. Chigusa, T. Moroi and Y. Shoji, State-of-the-Art Calculation of the Decay Rate of Electroweak Vacuum in the Standard Model, Phys. Rev. Lett. 119 (2017) 211801 [arXiv:1707.09301] [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].
J.S. Langer, Theory of the condensation point, Annals Phys. 41 (1967) 108 [INSPIRE].
J.S. Langer, Statistical theory of the decay of metastable states, Annals Phys. 54 (1969) 258 [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. D 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, Aspects of symmetry: selected Erice lectures, Cambridge University Press (1988).
I. Affleck, Quantum Statistical Metastability, Phys. Rev. Lett. 46 (1981) 388 [INSPIRE].
A.D. Linde, Fate of the False Vacuum at Finite Temperature: Theory and Applications, Phys. Lett. 100B (1981) 37 [INSPIRE].
A.D. Linde, Decay of the False Vacuum at Finite Temperature, Nucl. Phys. B 216 (1983) 421 [Erratum ibid. B 223 (1983) 544] [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].
B. Garbrecht and P. Millington, Green’s function method for handling radiative effects on false vacuum decay, Phys. Rev. D 91 (2015) 105021 [arXiv:1501.07466] [INSPIRE].
W.-Y. Ai, B. Garbrecht and P. Millington, Radiative effects on false vacuum decay in Higgs-Yukawa theory, Phys. Rev. D 98 (2018) 076014 [arXiv:1807.03338] [INSPIRE].
A.D. Plascencia and C. Tamarit, Convexity, gauge-dependence and tunneling rates, JHEP 10 (2016) 099 [arXiv:1510.07613] [INSPIRE].
W.Y. Ai, B. Garbrecht, C. Tamarit, Real-time picture of quantum tunneling in quantum field theory using functional methods, to appear.
J.B. Hartle and S.W. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
Y. Takahasi and H. Umezawa, Thermo field dynamics, Collect. Phenom. 2 (1975) 55.
A. Einstein and N. Rosen, The Particle Problem in the General Theory of Relativity, Phys. Rev. 48 (1935) 73 [INSPIRE].
S.W. Hawking, Gravitational Instantons, Phys. Lett. A 60 (1977) 81 [INSPIRE].
M. Spradlin, A. Strominger and A. Volovich, Les Houches lectures on de Sitter space, in Unity from duality: Gravity, gauge theory and strings. Proceedings, NATO Advanced Study Institute, Euro Summer School, 76th session, Les Houches, France, July 30–August 31, 2001, pp. 423–453 (2001) [hep-th/0110007] [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cim. 4 (1972) 737 [INSPIRE].
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
S.D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
A. Einstein, B. Podolsky and N. Rosen, Can quantum mechanical description of physical reality be considered complete?, Phys. Rev. 47 (1935) 777 [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1812.06962
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Ai, WY. Correspondence between thermal and quantum vacuum transitions around horizons. J. High Energ. Phys. 2019, 164 (2019). https://doi.org/10.1007/JHEP03(2019)164
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2019)164