Black holes, oscillating instantons and the Hawking-Moss transition
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Springer
Received: March 17, Revised: May 15, Accepted: June 12, Published: July 3,
2020 2020 2020 2020
Ruth Gregory,a,b,c Ian G. Mossd and Naritaka Oshitac a
Institute for Particle Physics Phenomenology, Department of Physics, Durham University, South Road, Durham, DH1 3LE, U.K. b Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, U.K. c Perimeter Institute, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada d School of Mathematics, Statistics and Physics, Newcastle University, Newcastle Upon Tyne, NE1 7RU, U.K.
E-mail: [email protected], [email protected], [email protected] Abstract: Static oscillating bounces in Schwarzschild de Sitter spacetime are investigated. The oscillating bounce with many oscillations gives a super-thick bubble wall, for which the total vacuum energy increases while the mass of the black hole decreases due to the conservation of Arnowitt-Deser-Misner (ADM) mass. We show that the transition rate of such an “up-tunneling” consuming the seed black hole is higher than that of the HawkingMoss transition. The correspondence of analyses in the static and global coordinates in the Euclidean de Sitter space is also investigated. Keywords: Black Holes, Solitons Monopoles and Instantons ArXiv ePrint: 2003.04927
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)024
JHEP07(2020)024
Black holes, oscillating instantons and the Hawking-Moss transition
Contents 1 Introduction
1
2 Oscillating bounce in static patch: dS and Nariai limits 2.1 Thermalons in de Sitter space 2.2 Thermalons near the Nariai limit
3 4 8 9 10 12
4 Hawking-Moss and oscillating bounces around a BH 4.1 HM bounce in the presence of a BH 4.2 Comparison between the oscillating bounce and BHHM bounce
13 15 18
5 Conclusion
18
1
Introduction
Cosmological phase transitions involving supercooling and the formation of bubbles may have played an important role in the early universe. In the case of extreme supercooling, the phase transition involves a quantum transition of a scalar field through a potential barrier from a false vacuum state to a true vacuum state. The vacuum decay rate is conventionally described in terms of an instanton, or bounce solution, to the field equations in imaginary time [1–3]. In an interesting recent twist, primordial black holes [4–9] and horizonless compact objects [10, 11] have been shown to act as nucleation seeds for true vacuum bubbles, and significantly enhance the decay rate (see also early work [12–14]). There is however another type of tunnelling solution — the Hawking-Moss (HM) instanton [15] — that is relevant for relatively flat potentials, and the aim of this paper is to explore how seeded nucleation proceeds in this case. We are interested in situations where gravitational effects on bubble nucleation are important. This was first investigated by Coleman and de Luccia (CDL) [3], who looked at bounce solutions to the Einstein-scalar system with O(4) symmetry. Shortly after their work, in t
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