Abstract
We consider the static charged black hole bomb system, originally designed for a (uncharged) rotating superradiant system by Press and Teukolsky. A charged scalar field confined in a Minkowski cavity with a Maxwell gauge field has a quantized spectrum of normal modes that can fit inside the box. Back-reacting non-linearly these normal modes, we find the hairy solitons, a.k.a boson stars (depending on the chosen U(1) gauge), of the theory. The scalar condensate is totally confined inside the box and, outside it, we have the Reissner-Nordström solution. The Israel junction conditions at the box surface layer determine the stress tensor that the box must have to confine the scalar hair. Some of these horizonless hairy solutions exist for any value of the scalar field charge and not only above the natural critical charges of the theory (namely, the critical charges for the onset of the near-horizon and superradiant instabilities of the Reissner-Nordström black hole). However, the ground state solutions have a non-trivial intricate phase diagram with a main and a secondary family of solitons (some with a Chandrasekhar mass limit but others without) and there are a third and a fourth critical scalar field charges where the soliton spectra changes radically. Most of these intricate properties are not captured by a higher order perturbative analysis of the problem where we simply back-react a normal mode of the system.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. H. Press and S. A. Teukolsky, Floating Orbits, Supermdiant Scattering and the Black-hole Bomb, Nature 238 (1972) 211 [INSPIRE].
V. Cardoso, O. J. C. Dias, J. P. S. Lemos and S. Yoshida, The Black hole bomb and supermdiant instabilities, Phys. Rev. D 70 (2004) 044039 [Erratum ibid. 70 (2004) 049903] [hep-th/0404096] [INSPIRE].
G. Denardo and R. Ruffini, On the energetics of Reissner Nordstrom geometries, Phys. Lett. B 45 (1973) 259 [INSPIRE].
O. J. C. Dias and R. Masachs, Evading no-hair theorems: hairy black holes in a Minkowski box, Phys. Rev. D 97 (2018) 124030 [arXiv:1802.01603] [INSPIRE].
S. L. Liebling and C. Palenzuela, Dynamical Boson Stars, Living Rev. Rel. 15 (2012) 6 [arXiv:1202.5809] [INSPIRE].
S. A. Gentle, M. Rangamani and B. Withers, A Soliton Menagerie in AdS, JHEP 05 (2012) 106 [arXiv:1112.3979] [INSPIRE].
P. Basu, J. Bhattacharya, S. Bhattacharyya, R. Loganayagam, S. Minwalla and V. Umesh, Small Hairy Black Holes in Global AdS Spacetime, JHEP 10 (2010) 045 [arXiv:1003.3232] [INSPIRE].
S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small Hairy Black Holes in AdS5xS5, JHEP 11 (2011) 035 [arXiv:1005.1287] [INSPIRE].
O. J. C. Dias, P. Figueras, S. Minwalla, P. Mitra, R. Monteiro and J. E. Santos, Hairy black holes and solitons in global AdS5, JHEP 08 (2012) 117 [arXiv:1112.4447] [INSPIRE].
R. Arias, J. Mas and A. Serantes, Stability of charged global AdS4 spacetimes, JHEP 09 (2016) 024 [arXiv:1606.00830] [INSPIRE].
J. Markeviciute and J. E. Santos, Hairy black holes in AdS5 × S5, JHEP 06 (2016) 096 [arXiv:1602.03893] [INSPIRE].
J. Markeviciute, Rotating Hairy Black Holes in AdS5 × S5, JHEP 03 (2019) 110 [arXiv:1809.04084] [INSPIRE].
O. J. C. Dias and R. Masachs, Hairy black holes and the endpoint of AdS4 charged superradiance, JHEP 02 (2017) 128 [arXiv:1610.03496] [INSPIRE].
S. S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S. A. Hartnoll, C. P. Herzog and G. T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S. A. Hartnoll, C. P. Herzog and G. T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
O. J. C. Dias, R. Monteiro, H. S. Reall and J. E. Santos, A Scalar field condensation instability of rotating anti-de Sitter black holes, JHEP 11 (2010) 036 [arXiv:1007.3745] [INSPIRE].
O. J. C. Dias and R. Masachs, Charged black hole bombs in a Minkowski cavity, Class. Quant. Grav. 35 (2018) 184001 [arXiv:1801.10176] [INSPIRE].
A. Davey, O. J. C. Dias and P. Rodgers, Phase diagram of the charged black hole bomb system, to appear.
D. Wiltshire, Spherically symmetric solutions of einstein-maxwell theory with a gauss-bonnet term, Phys. Lett. B 169 (1986) 36.
R. D’Inverno, Introducing Einstein’s Relativity, Clarendon Press, Oxford U.K. (1992).
R. L. Arnowitt, S. Deser and C. W. Misner, The Dynamics of general relativity, Gen. Rel. Grav. 40 (2008) 1997 [gr-qc/0405109] [INSPIRE].
J. D. Brown and J. W. York, Jr., Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [INSPIRE].
R. M. Wald, General relativity, Chicago University Press, Chicago U.S.A. (1984).
O. J. C. Dias, J. E. Santos and B. Way, Numerical Methods for Finding Stationary Gravitational Solutions, Class. Quant. Grav. 33 (2016) 133001 [arXiv:1510.02804] [INSPIRE].
W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B 44S10 (1966) 1 [Erratum ibid. 48 (1967) 463] [INSPIRE].
W. Israel, Discontinuities in spherically symmetric gravitational fields and shells of radiation, Proc. Roy. Soc. Lond. A 248 (1958) 404, http://rspa.royalsocietypublishing.org/content/royprsa/248/1254/404.full.pdf.
K. Kuchar, Charged shells in general relativity and their gravitational collapse, Czech. J. Phys. B B18 (1968) 435.
C. Barrabes and W. Israel, Thin shells in general relativity and cosmology: The Lightlike limit, Phys. Rev. D 43 (1991) 1129 [INSPIRE].
C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Freeman and Co., San Francisco U.S.A. (1973).
C. A. R. Herdeiro, J. C. Degollado and H. F. Rúnarsson, Rapid growth of superradiant instabilities for charged black holes in a cavity, Phys. Rev. D 88 (2013) 063003 [arXiv:1305.5513] [INSPIRE].
S. Hod, Analytic treatment of the charged black-hole-mirror bomb in the highly explosive regime, Phys. Rev. D 88 (2013) 064055 [arXiv:1310.6101] [INSPIRE].
J. C. Degollado and C. A. R. Herdeiro, Time evolution of superradiant instabilities for charged black holes in a cavity, Phys. Rev. D 89 (2014) 063005 [arXiv:1312.4579] [INSPIRE].
S. Hod, Resonance spectra of caged black holes, Eur. Phys. J. C 74 (2014) 3137 [arXiv:1410.4567] [INSPIRE].
R. Li, J.-K. Zhao and Y.-M. Zhang, Superradiant Instability of D-Dimensional Reissner—Nordström Black Hole Mirror System, Commun. Theor. Phys. 63 (2015) 569 [arXiv:1404.6309] [INSPIRE].
S. Hod, The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field, Phys. Lett. B 755 (2016) 177 [arXiv:1606.00444] [INSPIRE].
O. Fierro, N. Grandi and J. Oliva, Superradiance of charged black holes in Einstein–Gauss–Bonnet gravity, Class. Quant. Grav. 35 (2018) 105007 [arXiv:1708.06037] [INSPIRE].
R. Li and J. Zhao, Superradiant instability of charged scalar field in stringy black hole mirror system, Eur. Phys. J. C 74 (2014) 3051 [arXiv:1403.7279] [INSPIRE].
R. Li and J. Zhao, Numerical study of superradiant instability for charged stringy black hole–mirror system, Phys. Lett. B 740 (2015) 317 [arXiv:1412.1527] [INSPIRE].
R. Li, Y. Tian, H.-b. Zhang and J. Zhao, Time domain analysis of superradiant instability for the charged stringy black hole–mirror system, Phys. Lett. B 750 (2015) 520 [arXiv:1506.04267] [INSPIRE].
R. Li, J. Zhao, X. Wu and Y. Zhang, Scalar clouds in charged stringy black hole-mirror system, Eur. Phys. J. C 75 (2015) 142 [arXiv:1501.07358] [INSPIRE].
S. R. Dolan, S. Ponglertsakul and E. Winstanley, Stability of black holes in Einstein-charged scalar field theory in a cavity, Phys. Rev. D 92 (2015) 124047 [arXiv:1507.02156] [INSPIRE].
S. Ponglertsakul, E. Winstanley and S. R. Dolan, Stability of gravitating charged-scalar solitons in a cavity, Phys. Rev. D 94 (2016) 024031 [arXiv:1604.01132] [INSPIRE].
S. Ponglertsakul and E. Winstanley, Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity, Phys. Lett. B 764 (2017) 87 [arXiv:1610.00135] [INSPIRE].
P. Basu, C. Krishnan and P. N. Bala Subramanian, Hairy Black Holes in a Box, JHEP 11 (2016) 041 [arXiv:1609.01208] [INSPIRE].
N. Sanchis-Gual, J. C. Degollado, P. J. Montero, J. A. Font and C. Herdeiro, Explosion and Final State of an Unstable Reissner-Nordström Black Hole, Phys. Rev. Lett. 116 (2016) 141101 [arXiv:1512.05358] [INSPIRE].
N. Sanchis-Gual, J. C. Degollado, C. Herdeiro, J. A. Font and P. J. Montero, Dynamical formation of a Reissner-Nordström black hole with scalar hair in a cavity, Phys. Rev. D 94 (2016) 044061 [arXiv:1607.06304] [INSPIRE].
N. Sanchis-Gual, J. C. Degollado, J. A. Font, C. Herdeiro and E. Radu, Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons, Class. Quant. Grav. 34 (2017) 165001 [arXiv:1611.02441] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2101.01203
Rights and permissions
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.
About this article
Cite this article
Dias, O.J.C., Masachs, R. & Rodgers, P. Boson stars and solitons confined in a Minkowski box. J. High Energ. Phys. 2021, 236 (2021). https://doi.org/10.1007/JHEP04(2021)236
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)236