Abstract
We consider the effect of inhomogeneities on the rate of false vacuum decay. Modelling the inhomogeneity by a black hole, we construct explicit Euclidean instantons which describe the nucleation of a bubble of true vacuum centred on the inhomogeneity. We find that inhomogeneity significantly enhances the nucleation rate over that of the Coleman-de Luccia instanton — the black hole acts as a nucleation site for the bubble. The effect is larger than previously believed due to the contributions to the action from conical singularities. For a sufficiently low initial mass, the original black hole is replaced by flat space during this process, as viewed by a single causal patch observer. Increasing the initial mass, we find a critical value above which a black hole remnant survives the process. This resulting black hole can have a higher mass than the original black hole, but always has a lower entropy. We compare the process to bubble-to-bubble transitions, where there is a semi-classical Lorentzian description in the WKB approximation.
References
- [1]
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].
- [2]
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].
- [3]
A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
- [4]
M.S. Turner and F. Wilczek, Might our vacuum be metastable?, Nature 298 (1982) 633 [INSPIRE].
- [5]
W.A. Hiscock, Can black holes nucleate vacuum phase transitions?, Phys. Rev. D 35 (1987) 1161 [INSPIRE].
- [6]
V.A. Berezin, V.A. Kuzmin and I.I. Tkachev, O(3) Invariant Tunneling in General Relativity, Phys. Lett. B 207 (1988) 397 [INSPIRE].
- [7]
V.A. Berezin, V.A. Kuzmin and I.I. Tkachev, Black holes initiate false vacuum decay, Phys. Rev. D 43 (1991) 3112 [INSPIRE].
- [8]
I.G. Moss, Black hole bubbles, Phys. Rev. D 32 (1985) 1333 [INSPIRE].
- [9]
C. Cheung and S. Leichenauer, Limits on New Physics from Black Holes, arXiv:1309.0530 [INSPIRE].
- [10]
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
- [11]
H. Nariai, On some static solutions of Einstein’s gravitational field equations in a spherically symmetric case, Sci. Rept. Tohoku Univ. 34 (1950) 160.
- [12]
H. Nariai, On a new cosmological solution of Einstein’s field equations of gravitation, Sci. Rept. Tohoku Univ. 35 (1951) 46.
- [13]
S.W. Hawking and N. Turok, Open inflation without false vacua, Phys. Lett. B 425 (1998) 25 [hep-th/9802030] [INSPIRE].
- [14]
N. Turok and S.W. Hawking, Open inflation, the four form and the cosmological constant, Phys. Lett. B 432 (1998) 271 [hep-th/9803156] [INSPIRE].
- [15]
G.W. Gibbons and S.W. Hawking, Classification of Gravitational Instanton Symmetries, Commun. Math. Phys. 66 (1979) 291 [INSPIRE].
- [16]
J. Garriga and A. Megevand, Decay of de Sitter vacua by thermal activation, Int. J. Theor. Phys. 43 (2004) 883 [hep-th/0404097] [INSPIRE].
- [17]
E. Farhi, A.H. Guth and J. Guven, Is It Possible to Create a Universe in the Laboratory by Quantum Tunneling?, Nucl. Phys. B 339 (1990) 417 [INSPIRE].
- [18]
W. Fischler, D. Morgan and J. Polchinski, Quantum Nucleation of False Vacuum Bubbles, Phys. Rev. D 41 (1990) 2638 [INSPIRE].
- [19]
W. Fischler, D. Morgan and J. Polchinski, Quantization of False Vacuum Bubbles: A Hamiltonian Treatment of Gravitational Tunneling, Phys. Rev. D 42 (1990) 4042 [INSPIRE].
- [20]
A. Aguirre and M.C. Johnson, Dynamics and instability of false vacuum bubbles, Phys. Rev. D 72 (2005) 103525 [gr-qc/0508093] [INSPIRE].
- [21]
A. Aguirre and M.C. Johnson, Two tunnels to inflation, Phys. Rev. D 73 (2006) 123529 [gr-qc/0512034] [INSPIRE].
- [22]
W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cimento Soc. Ital. Phys. B 44 (1966) 4349.
- [23]
P. Bowcock, C. Charmousis and R. Gregory, General brane cosmologies and their global space-time structure, Class. Quant. Grav. 17 (2000) 4745 [hep-th/0007177] [INSPIRE].
- [24]
F. Mellor and I. Moss, Black Holes and Quantum Wormholes, Phys. Lett. B 222 (1989) 361 [INSPIRE].
- [25]
F. Mellor and I. Moss, Black Holes and Gravitational Instantons, Class. Quant. Grav. 6 (1989) 1379 [INSPIRE].
- [26]
F. Dowker, J.P. Gauntlett, D.A. Kastor and J.H. Traschen, Pair creation of dilaton black holes, Phys. Rev. D 49 (1994) 2909 [hep-th/9309075] [INSPIRE].
- [27]
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].
- [28]
R.P. Geroch and J.H. Traschen, Strings and Other Distributional Sources in General Relativity, Phys. Rev. D 36 (1987) 1017 [INSPIRE].
- [29]
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].
- [30]
D.V. Fursaev and S.N. Solodukhin, On the description of the Riemannian geometry in the presence of conical defects, Phys. Rev. D 52 (1995) 2133 [hep-th/9501127] [INSPIRE].
- [31]
D.N. Page, Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole, Phys. Rev. D 13 (1976) 198 [INSPIRE].
- [32]
C. Charmousis and R. Gregory, Axisymmetric metrics in arbitrary dimensions, Class. Quant. Grav. 21 (2004) 527 [gr-qc/0306069] [INSPIRE].
- [33]
C. Charmousis, Dilaton space-times with a Liouville potential, Class. Quant. Grav. 19 (2002) 83 [hep-th/0107126] [INSPIRE].
- [34]
S. Chadburn and R. Gregory, Time dependent black holes and scalar hair, arXiv:1304.6287 [INSPIRE].
- [35]
N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, The Hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [INSPIRE].
- [36]
L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
- [37]
P. Kanti, Black holes in theories with large extra dimensions: A Review, Int. J. Mod. Phys. A 19 (2004) 4899 [hep-ph/0402168] [INSPIRE].
- [38]
R. Gregory and A. Padilla, Brane world instantons, Class. Quant. Grav. 19 (2002) 279 [hep-th/0107108] [INSPIRE].
- [39]
R. Gregory, Braneworld black holes, Lect. Notes Phys. 769 (2009) 259 [arXiv:0804.2595] [INSPIRE].
- [40]
P. Figueras and T. Wiseman, Gravity and large black holes in Randall-Sundrum II braneworlds, Phys. Rev. Lett. 107 (2011) 081101 [arXiv:1105.2558] [INSPIRE].
- [41]
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
- [42]
V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].
- [43]
A. Westphal, Lifetime of Stringy de Sitter Vacua, JHEP 01 (2008) 012 [arXiv:0705.1557] [INSPIRE].
- [44]
S. de Alwis, R. Gupta, E. Hatefi and F. Quevedo, Stability, Tunneling and Flux Changing de Sitter Transitions in the Large Volume String Scenario, JHEP 11 (2013) 179 [arXiv:1308.1222] [INSPIRE].
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Gregory, R., Moss, I.G. & Withers, B. Black holes as bubble nucleation sites. J. High Energ. Phys. 2014, 81 (2014). https://doi.org/10.1007/JHEP03(2014)081
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Keywords
- Cosmology of Theories beyond the SM
- Black Holes
- Solitons Monopoles and Instantons