# Black holes as bubble nucleation sites

- 352 Downloads
- 22 Citations

## 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.

## Keywords

Cosmology of Theories beyond the SM Black Holes Solitons Monopoles and Instantons## 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]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].ADSGoogle Scholar - [3]A.H. Guth,
*The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems*,*Phys. Rev.***D 23**(1981) 347 [INSPIRE].ADSGoogle Scholar - [4]M.S. Turner and F. Wilczek,
*Might our vacuum be metastable?*,*Nature***298**(1982) 633 [INSPIRE].ADSCrossRefGoogle Scholar - [5]W.A. Hiscock,
*Can black holes nucleate vacuum phase transitions?*,*Phys. Rev.***D 35**(1987) 1161 [INSPIRE].ADSMathSciNetGoogle Scholar - [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].ADSCrossRefMathSciNetGoogle Scholar - [7]V.A. Berezin, V.A. Kuzmin and I.I. Tkachev,
*Black holes initiate false vacuum decay*,*Phys. Rev.***D 43**(1991) 3112 [INSPIRE].ADSGoogle Scholar - [8]
- [9]
- [10]S.R. Coleman and F. De Luccia,
*Gravitational Effects on and of Vacuum Decay*,*Phys. Rev.***D 21**(1980) 3305 [INSPIRE].ADSGoogle Scholar - [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.ADSMathSciNetGoogle Scholar - [12]H. Nariai,
*On a new cosmological solution of Einstein*’*s field equations of gravitation*,*Sci. Rept. Tohoku Univ.***35**(1951) 46.MathSciNetGoogle Scholar - [13]S.W. Hawking and N. Turok,
*Open inflation without false vacua*,*Phys. Lett.***B 425**(1998) 25 [hep-th/9802030] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar - [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].ADSCrossRefMathSciNetGoogle Scholar - [15]G.W. Gibbons and S.W. Hawking,
*Classification of Gravitational Instanton Symmetries*,*Commun. Math. Phys.***66**(1979) 291 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar - [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].CrossRefzbMATHGoogle Scholar - [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].ADSCrossRefMathSciNetGoogle Scholar - [18]W. Fischler, D. Morgan and J. Polchinski,
*Quantum Nucleation of False Vacuum Bubbles*,*Phys. Rev.***D 41**(1990) 2638 [INSPIRE].ADSMathSciNetGoogle Scholar - [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].ADSMathSciNetGoogle Scholar - [20]A. Aguirre and M.C. Johnson,
*Dynamics and instability of false vacuum bubbles*,*Phys. Rev.***D 72**(2005) 103525 [gr-qc/0508093] [INSPIRE].ADSGoogle Scholar - [21]A. Aguirre and M.C. Johnson,
*Two tunnels to inflation*,*Phys. Rev.***D 73**(2006) 123529 [gr-qc/0512034] [INSPIRE].ADSGoogle Scholar - [22]W. Israel,
*Singular hypersurfaces and thin shells in general relativity*,*Nuovo Cimento Soc. Ital. Phys. B***44**(1966) 4349.Google Scholar - [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].ADSCrossRefzbMATHMathSciNetGoogle Scholar - [24]F. Mellor and I. Moss,
*Black Holes and Quantum Wormholes*,*Phys. Lett.***B 222**(1989) 361 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar - [25]F. Mellor and I. Moss,
*Black Holes and Gravitational Instantons*,*Class. Quant. Grav.***6**(1989) 1379 [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar - [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].ADSMathSciNetGoogle Scholar - [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].ADSGoogle Scholar - [28]R.P. Geroch and J.H. Traschen,
*Strings and Other Distributional Sources in General Relativity*,*Phys. Rev.***D 36**(1987) 1017 [INSPIRE].ADSMathSciNetGoogle Scholar - [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].ADSCrossRefzbMATHMathSciNetGoogle Scholar - [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].ADSMathSciNetGoogle Scholar - [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].ADSGoogle Scholar - [32]C. Charmousis and R. Gregory,
*Axisymmetric metrics in arbitrary dimensions*,*Class. Quant. Grav.***21**(2004) 527 [gr-qc/0306069] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar - [33]C. Charmousis,
*Dilaton space-times with a Liouville potential*,*Class. Quant. Grav.***19**(2002) 83 [hep-th/0107126] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar - [34]
- [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].ADSCrossRefGoogle Scholar - [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].ADSCrossRefzbMATHMathSciNetGoogle Scholar - [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].ADSCrossRefMathSciNetGoogle Scholar - [38]R. Gregory and A. Padilla,
*Brane world instantons*,*Class. Quant. Grav.***19**(2002) 279 [hep-th/0107108] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar - [39]R. Gregory,
*Braneworld black holes*,*Lect. Notes Phys.***769**(2009) 259 [arXiv:0804.2595] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar - [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].ADSCrossRefGoogle Scholar - [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].ADSMathSciNetGoogle Scholar - [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].ADSCrossRefMathSciNetGoogle Scholar - [43]A. Westphal,
*Lifetime of Stringy de Sitter Vacua*,*JHEP***01**(2008) 012 [arXiv:0705.1557] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar - [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].ADSCrossRefGoogle Scholar