Erratum to: Vacuum decays around spinning black holes
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Received: September 4, 2020 Accepted: September 18, 2020 Published: October 19, 2020
Erratum: Vacuum decays around spinning black holes Naritaka Oshita,a Kazushige Uedab and Masahide Yamaguchic a
E-mail: [email protected], [email protected], [email protected] Erratum to: JHEP01(2020)015 ArXiv ePrint: 1909.01378 The published work relies on the diagonalized metric shown in eq. (3.7), and it was mentioned that eq. (3.7) is obtained by the transformation dφ → dψ − g˜φt /˜ gφφ dλ. However, the diagonalized metric is not exactly obtained by the transformation but is valid approximately, which was missed in the original paper. This does not affect our results and conclusion as is explained below. The angular velocity, ω ≡ −˜ gφt /˜ gφφ has r and θ-dependence, and therefore, the correct transformation should be dφ → dψ + ωdλ + (∂r ω)λdr + (∂θ ω)λdθ. The last term is strongly suppressed by ∂θ ω ∼ −4M a3 ∆/r7 , which leads to negligible corrections to g˜µν outside the horizon. The dr-term in the transformation also gives a negligible correction, C, to the induced metric in eq. (3.11): ds2 = (−1 + C)dτ 2 + gθθ dθ2 + gψψ dψ 2 , 5 ˙ ∼ −48M 2 a2 Rλ/R ˙ with C ∼ 4R2 ω(∂r ω)Rλ ,
(1) (2)
where |C| 1 holds for R ≥ Rmin . Note that although R ∼ M for R ' Rmin , R˙ ' 0 suppresses the factor C there. We should also emphasize that λ . Rmax is assumed since only one Euclidean period is taken into account in the calculation of the Euclidean action.
Acknowledgments We are very grateful to Ruth Gregory for pointing out this error. 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.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)122
JHEP10(2020)122
Perimeter Institute, 31 Caroline St, Waterloo, Ontario N2L 2Y5, Canada b Graduate School of Science Hiroshima University, 1-3-1 Kagami Yama, Higashi-Hiroshima, 739-8526, Japan c Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
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