Abstract
We consider the Friedberg-Lee-Sirlin model minimally coupled to Einstein gravity in four spacetime dimensions. The renormalizable Friedberg-Lee-Sirlin model consists of two interacting scalar fields, where the mass of the complex scalar field results from the interaction with the real scalar field which has a finite vacuum expectation value. We here study a new family of self-gravitating axially-symmetric, rotating boson stars in this model. In the flat space limit these boson stars tend to the corresponding Q-balls. Subject to the usual synchronization condition, the model admits spinning hairy black hole solutions with two different types of scalar hair. We here investigate parity-even and parity-odd boson stars and their associated hairy black holes. We explore the domain of existence of the solutions and address some of their physical properties. The solutions exhibit close similarity to the corresponding boson stars and Kerr black holes with synchronised scalar hair in the O(3)-sigma model coupled to Einstein gravity and to the corresponding solutions in the Einstein-Klein-Gordon theory with a complex scalar field, where the latter are recovered in a limit.
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References
D.J. Kaup, Klein-Gordon Geon, Phys. Rev.172 (1968) 1331 [INSPIRE].
R. Ruffini and S. Bonazzola, Systems of selfgravitating particles in general relativity and the concept of an equation of state, Phys. Rev.187 (1969) 1767 [INSPIRE].
H. Lückock and I. Moss, Black Holes Have Skyrmion Hair, Phys. Lett.B 176 (1986) 341 [INSPIRE].
S. Droz, M. Heusler and N. Straumann, New black hole solutions with hair, Phys. Lett.B 268 (1991) 371 [INSPIRE].
P. Bizon and T. Chmaj, Gravitating skyrmions, Phys. Lett.B 297 (1992) 55 [INSPIRE].
R. Bartnik and J. Mckinnon, Particle-Like Solutions of the Einstein Yang-Mills Equations, Phys. Rev. Lett.61 (1988) 141 [INSPIRE].
K.-M. Lee, V.P. Nair and E.J. Weinberg, Black holes in magnetic monopoles, Phys. Rev.D 45 (1992) 2751 [hep-th/9112008] [INSPIRE].
P. Breitenlohner, P. Forgacs and D. Maison, Gravitating monopole solutions, Nucl. Phys.B 383 (1992) 357 [INSPIRE].
B.R. Greene, S.D. Mathur and C.M. O’Neill, Eluding the no hair conjecture: Black holes in spontaneously broken gauge theories, Phys. Rev.D 47 (1993) 2242 [hep-th/9211007] [INSPIRE].
P. Breitenlohner, P. Forgacs and D. Maison, Gravitating monopole solutions. 2, Nucl. Phys.B 442 (1995) 126 [gr-qc/9412039] [INSPIRE].
R. Friedberg, T.D. Lee and A. Sirlin, A Class of Scalar-Field Soliton Solutions in Three Space Dimensions, Phys. Rev.D 13 (1976) 2739 [INSPIRE].
S.R. Coleman, Q Balls, Nucl. Phys.B 262 (1985) 263 [Erratum ibid.B 269 (1986) 744] [INSPIRE].
G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl. Phys.B 79 (1974) 276 [INSPIRE].
A.M. Polyakov, Particle Spectrum in the Quantum Field Theory, JETP Lett.20 (1974) 194 [INSPIRE].
F.R. Klinkhamer and N.S. Manton, A Saddle Point Solution in the Weinberg-Salam Theory, Phys. Rev.D 30 (1984) 2212 [INSPIRE].
T.H.R. Skyrme, A Nonlinear field theory, Proc. Roy. Soc. Lond.A 260 (1961) 127 [INSPIRE].
R. Friedberg, T.D. Lee and Y. Pang, Mini-soliton stars, Phys. Rev.D 35 (1987) 3640 [INSPIRE].
R. Friedberg, T.D. Lee and Y. Pang, Scalar Soliton Stars and Black Holes, Phys. Rev.D 35 (1987) 3658 [INSPIRE].
B. Kleihaus, J. Kunz and M. List, Rotating boson stars and Q-balls, Phys. Rev.D 72 (2005) 064002 [gr-qc/0505143] [INSPIRE].
B. Kleihaus, J. Kunz, M. List and I. Schaffer, Rotating Boson Stars and Q-Balls. II. Negative Parity and Ergoregions, Phys. Rev.D 77 (2008) 064025 [arXiv:0712.3742] [INSPIRE].
M.S. Volkov and D.V. Galtsov, NonAbelian Einstein Yang-Mills black holes, JETP Lett.50 (1989) 346 [INSPIRE].
R. Ruffini and J.A. Wheeler, Introducing the black hole, Phys. Today24 (1971) 30.
M.S. Volkov and D.V. Gal’tsov, Gravitating nonAbelian solitons and black holes with Yang-Mills fields, Phys. Rept.319 (1999) 1 [hep-th/9810070] [INSPIRE].
C.A.R. Herdeiro and E. Radu, Asymptotically flat black holes with scalar hair: a review, Int. J. Mod. Phys.D 24 (2015) 1542014 [arXiv:1504.08209] [INSPIRE].
M.S. Volkov, Hairy black holes in the XX-th and XXI-st centuries, in Proceedings, 14th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories (MG14) (In 4 Volumes): Rome, Italy, July 12-18, 2015, vol. 2, pp. 1779-1798, 2017, arXiv:1601.08230 [INSPIRE].
I. Pena and D. Sudarsky, Do collapsed boson stars result in new types of black holes?, Class. Quant. Grav.14 (1997) 3131 [INSPIRE].
S. Hod, No-go theorem for static boson stars, Phys. Lett.B 778 (2018) 239 [arXiv:1902.05230] [INSPIRE].
C. Adam, O. Kichakova, Ya. Shnir and A. Wereszczynski, Hairy black holes in the general Skyrme model, Phys. Rev.D 94 (2016) 024060 [arXiv:1605.07625] [INSPIRE].
S.B. Gudnason, M. Nitta and N. Sawado, Black hole Skyrmion in a generalized Skyrme model, JHEP09 (2016) 055 [arXiv:1605.07954] [INSPIRE].
I. Perapechka and Y. Shnir, Generalized Skyrmions and hairy black holes in asymptotically AdS 4spacetime, Phys. Rev.D 95 (2017) 025024 [arXiv:1612.01914] [INSPIRE].
Y. Kobayashi, M. Kasai and T. Futamase, Does a boson star rotate?, Phys. Rev.D 50 (1994) 7721 [INSPIRE].
F.E. Schunck and E.W. Mielke, Rotating boson star as an effective mass torus in general relativity, Phys. Lett.A 249 (1998) 389 [INSPIRE].
F.D. Ryan, Spinning boson stars with large selfinteraction, Phys. Rev.D 55 (1997) 6081 [INSPIRE].
S. Yoshida and Y. Eriguchi, Rotating boson stars in general relativity, Phys. Rev.D 56 (1997) 762 [INSPIRE].
T. Ioannidou, B. Kleihaus and J. Kunz, Spinning gravitating skyrmions, Phys. Lett.B 643 (2006) 213 [gr-qc/0608110] [INSPIRE].
B. Kleihaus, J. Kunz and U. Neemann, Gravitating stationary dyons and rotating vortex rings, Phys. Lett.B 623 (2005) 171 [gr-qc/0507047] [INSPIRE].
B. Kleihaus, J. Kunz, F. Navarro-Lerida and U. Neemann, Stationary Dyonic Regular and Black Hole Solutions, Gen. Rel. Grav.40 (2008) 1279 [arXiv:0705.1511] [INSPIRE].
C. Herdeiro, I. Perapechka, E. Radu and Ya. Shnir, Gravitating solitons and black holes with synchronised hair in the four dimensional O(3) σ-model, JHEP02 (2019) 111 [arXiv:1811.11799] [INSPIRE].
B. Kleihaus and J. Kunz, Rotating hairy black holes, Phys. Rev. Lett.86 (2001) 3704 [gr-qc/0012081] [INSPIRE].
B. Kleihaus, J. Kunz and F. Navarro-Lerida, Rotating Einstein-Yang-Mills black holes, Phys. Rev.D 66 (2002) 104001 [gr-qc/0207042] [INSPIRE].
B. Kleihaus, J. Kunz and F. Navarro-Lerida, Rotating dilaton black holes with hair, Phys. Rev.D 69 (2004) 064028 [gr-qc/0306058] [INSPIRE].
B. Kleihaus, J. Kunz and F. Navarro-Lerida, Stationary black holes with static and counter rotating horizons, Phys. Rev.D 69 (2004) 081501 [gr-qc/0309082] [INSPIRE].
B. Kleihaus, J. Kunz and F. Navarro-Lerida, Rotating black holes with monopole hair, Phys. Lett.B 599 (2004) 294 [gr-qc/0406094] [INSPIRE].
B. Kleihaus, J. Kunz and F. Navarro-Lerida, Rotating black holes with non-Abelian hair, Class. Quant. Grav.33 (2016) 234002 [arXiv:1609.07357] [INSPIRE].
S. Hod, Stationary Scalar Clouds Around Rotating Black Holes, Phys. Rev.D 86 (2012) 104026 [Erratum ibid.D 86 (2012) 129902] [arXiv:1211.3202] [INSPIRE].
C.A.R. Herdeiro and E. Radu, Kerr black holes with scalar hair, Phys. Rev. Lett.112 (2014) 221101 [arXiv:1403.2757] [INSPIRE].
C. Herdeiro and E. Radu, Ergosurfaces for Kerr black holes with scalar hair, Phys. Rev.D 89 (2014) 124018 [arXiv:1406.1225] [INSPIRE].
C. Herdeiro and E. Radu, Construction and physical properties of Kerr black holes with scalar hair, Class. Quant. Grav.32 (2015) 144001 [arXiv:1501.04319] [INSPIRE].
S. Hod, Kerr-Newman black holes with stationary charged scalar clouds, Phys. Rev.D 90 (2014) 024051 [arXiv:1406.1179] [INSPIRE].
C.L. Benone, L.C.B. Crispino, C. Herdeiro and E. Radu, Kerr-Newman scalar clouds, Phys. Rev.D 90 (2014) 104024 [arXiv:1409.1593] [INSPIRE].
C. Herdeiro, E. Radu and H. Rúnarsson, Non-linear Q-clouds around Kerr black holes, Phys. Lett.B 739 (2014) 302 [arXiv:1409.2877] [INSPIRE].
C.A.R. Herdeiro and E. Radu, A new spin on black hole hair, Int. J. Mod. Phys.D 23 (2014) 1442014 [arXiv:1405.3696] [INSPIRE].
B. Kleihaus, J. Kunz and S. Yazadjiev, Scalarized Hairy Black Holes, Phys. Lett.B 744 (2015) 406 [arXiv:1503.01672] [INSPIRE].
C.A.R. Herdeiro, E. Radu and H. Rúnarsson, Kerr black holes with self-interacting scalar hair: hairier but not heavier, Phys. Rev.D 92 (2015) 084059 [arXiv:1509.02923] [INSPIRE].
C. Herdeiro, J. Kunz, E. Radu and B. Subagyo, Myers-Perry black holes with scalar hair and a mass gap: Unequal spins, Phys. Lett.B 748 (2015) 30 [arXiv:1505.02407] [INSPIRE].
C. Herdeiro, E. Radu and H. Rúnarsson, Kerr black holes with Proca hair, Class. Quant. Grav.33 (2016) 154001 [arXiv:1603.02687] [INSPIRE].
Y. Brihaye, C. Herdeiro and E. Radu, Inside black holes with synchronized hair, Phys. Lett.B 760 (2016) 279 [arXiv:1605.08901] [INSPIRE].
S. Hod, Extremal Kerr-Newman black holes with extremely short charged scalar hair, Phys. Lett.B 751 (2015) 177 [arXiv:1707.06246] [INSPIRE].
C. Herdeiro, J. Kunz, E. Radu and B. Subagyo, Probing the universality of synchronised hair around rotating black holes with Q-clouds, Phys. Lett.B 779 (2018) 151 [arXiv:1712.04286] [INSPIRE].
C. Herdeiro, I. Perapechka, E. Radu and Ya. Shnir, Skyrmions around Kerr black holes and spinning BHs with Skyrme hair, JHEP10 (2018) 119 [arXiv:1808.05388] [INSPIRE].
Y.-Q. Wang, Y.-X. Liu and S.-W. Wei, Excited Kerr black holes with scalar hair, Phys. Rev.D 99 (2019) 064036 [arXiv:1811.08795] [INSPIRE].
J.F.M. Delgado, C.A.R. Herdeiro and E. Radu, Kerr black holes with synchronised scalar hair and higher azimuthal harmonic index, Phys. Lett.B 792 (2019) 436 [arXiv:1903.01488] [INSPIRE].
J. Kunz, I. Perapechka and Ya. Shnir, Kerr black holes with parity-odd scalar hair, arXiv:1904.07630 [INSPIRE].
A. Levin and V. Rubakov, Q-balls with scalar charges, Mod. Phys. Lett.A 26 (2011) 409 [arXiv:1010.0030] [INSPIRE].
V. Loiko, I. Perapechka and Ya. Shnir, Q-balls without a potential, Phys. Rev.D 98 (2018) 045018 [arXiv:1805.11929] [INSPIRE].
M.S. Volkov and E. Wohnert, Spinning Q balls, Phys. Rev.D 66 (2002) 085003 [hep-th/0205157] [INSPIRE].
E. Radu and M.S. Volkov, Existence of stationary, non-radiating ring solitons in field theory: knots and vortons, Phys. Rept.468 (2008) 101 [arXiv:0804.1357] [INSPIRE].
Y. Brihaye and B. Hartmann, Angularly excited and interacting boson stars and Q-balls, Phys. Rev.D 79 (2009) 064013 [arXiv:0812.3968] [INSPIRE].
T. Tamaki and N. Sakai, Unified picture of Q-balls and boson stars via catastrophe theory, Phys. Rev.D 81 (2010) 124041 [arXiv:1105.1498] [INSPIRE].
L.G. Collodel, B. Kleihaus and J. Kunz, Excited Boson Stars, Phys. Rev.D 96 (2017) 084066 [arXiv:1708.02057] [INSPIRE].
I. Perapechka and Y. Shnir, Spinning gravitating Skyrmions in a generalized Einstein-Skyrme model, Phys. Rev.D 96 (2017) 125006 [arXiv:1710.06334] [INSPIRE].
G.C. Wick, Properties of Bethe-Salpeter Wave Functions, Phys. Rev.96 (1954) 1124 [INSPIRE].
R.E. Cutkosky, Solutions of a Bethe-Salpeter equations, Phys. Rev.96 (1954) 1135 [INSPIRE].
E. Ya. Nugaev and M.N. Smolyakov, Q-balls in the Wick-Cutkosky model, Eur. Phys. J.C 77 (2017) 118 [arXiv:1605.02056] [INSPIRE].
A.G. Panin and M.N. Smolyakov, Classical behaviour of Q-balls in the Wick-Cutkosky model, Eur. Phys. J.C 79 (2019) 150 [arXiv:1810.03558] [INSPIRE].
J. Kunz, E. Radu and B. Subagyo, Gravitating vortons as ring solitons in general relativity, Phys. Rev.D 87 (2013) 104022 [arXiv:1303.1003] [INSPIRE].
F.E. Schunck and E.W. Mielke, General relativistic boson stars, Class. Quant. Grav.20 (2003) R301 [arXiv:0801.0307] [INSPIRE].
T.D. Lee and Y. Pang, Stability of Mini-Boson Stars, Nucl. Phys.B 315 (1989) 477 [INSPIRE].
F.V. Kusmartsev, E.W. Mielke and F.E. Schunck, Gravitational stability of boson stars, Phys. Rev.D 43 (1991) 3895 [arXiv:0810.0696] [INSPIRE].
B. Kleihaus, J. Kunz and S. Schneider, Stable Phases of Boson Stars, Phys. Rev.D 85 (2012) 024045 [arXiv:1109.5858] [INSPIRE].
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Kunz, J., Perapechka, I. & Shnir, Y. Kerr black holes with synchronised scalar hair and boson stars in the Einstein-Friedberg-Lee-Sirlin model. J. High Energ. Phys. 2019, 109 (2019). https://doi.org/10.1007/JHEP07(2019)109
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DOI: https://doi.org/10.1007/JHEP07(2019)109