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  • Open Access

Two types of boson stars in the (3+1)-dimensional O(3) sigma-model

Jutta Kunz*

Aliaksei Mikhaliuk†

Yakov Shnir‡

  • BLTP, JINR, Dubna 141980, Moscow Region, Russia

  • *Contact author: jutta.kunz@uni-oldenburg.de
  • †Contact author: alekseybsu.mihalyuk@gmail.com
  • ‡Contact author: shnir@theor.jinr.ru
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Phys. Rev. D 113, 025009 – Published 21 January, 2026

DOI: https://doi.org/10.1103/8qwg-f9wz

Abstract

We investigate boson stars in an O(3) scalar field theory with a symmetry-breaking potential. By constructing numerically spherically symmetric solutions, we demonstrate that the model gives rise to a rich set of field configurations. The negative coupling constant of the scalar self-interactions allows for two types of boson stars: type I solutions represent the usual boson stars, which emerge from the vacuum as the boson frequency is decreased below the boson mass, whereas type II boson stars emerge from a set of static soliton solutions. Depending on the strength of the gravitational coupling constant, both types, or only one type, are present. At a critical set of coupling constants, both types undergo a bifurcation. There the spirals of both types disconnect from their branches and reconnect with each other, while the remaining branches of both types also reconnect with each other. Analogous features are seen for U(1)-gauged boson stars.

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References (52)

  1. D. J. Kaup, Phys. Rev. 172, 1331 (1968).
  2. D. A. Feinblum and W. A. McKinley, Phys. Rev. 168, 1445 (1968).
  3. R. Ruffini and S. Bonazzola, Phys. Rev. 187, 1767 (1969).
  4. M. Colpi, S. L. Shapiro, and I. Wasserman, Phys. Rev. Lett. 57, 2485 (1986).
  5. P. Jetzer, Phys. Rep. 220, 163 (1992).
  6. F. E. Schunck and E. W. Mielke, Classical Quantum Gravity 20, R301 (2003).
  7. S. L. Liebling and C. Palenzuela, Living Rev. Relativity 26, 1 (2023).
  8. Y. Shnir, Lect. Notes Phys. 1017, 347 (2023).
  9. R. Friedberg, T. D. Lee, and Y. Pang, Phys. Rev. D 35, 3658 (1987).
  10. B. Kleihaus, J. Kunz, and M. List, Phys. Rev. D 72, 064002 (2005).
  11. G. Rosen, J. Math. Phys. (N.Y.) 9, 996 (1968).
  12. R. Friedberg, T. D. Lee, and A. Sirlin, Phys. Rev. D 13, 2739 (1976).
  13. S. R. Coleman, Nucl. Phys. B262, 263 (1985); B269, 744(E) (1986).
  14. K. M. Lee, J. A. Stein-Schabes, R. Watkins, and L. M. Widrow, Phys. Rev. D 39, 1665 (1989).
  15. K. N. Anagnostopoulos, M. Axenides, E. G. Floratos, and N. Tetradis, Phys. Rev. D 64, 125006 (2001).
  16. I. E. Gulamov, E. Y. Nugaev, and M. N. Smolyakov, Phys. Rev. D 89, 085006 (2014).
  17. I. E. Gulamov, E. Y. Nugaev, A. G. Panin, and M. N. Smolyakov, Phys. Rev. D 92, 045011 (2015).
  18. J. Kunz, V. Loiko, and Y. Shnir, Phys. Rev. D 105, 085013 (2022).
  19. C. Herdeiro, I. Perapechka, E. Radu, and Y. Shnir, J. High Energy Phys. 02 (2019) 111.
  20. C. Adam, J. C. Mourelle, A. García Martín-Caro, and A. Wereszczynski, Phys. Rev. D 112, 023004 (2025).
  21. P. A. Cano, L. Machet, and C. Myin, Phys. Rev. D 109, 044043 (2024).
  22. Y. Verbin, Phys. Rev. D 76, 085018 (2007).
  23. L. A. Ferreira, A. Mikhaliuk, and Y. Shnir, Phys. Rev. D 112, 025003 (2025).
  24. U. Nucamendi and M. Salgado, Phys. Rev. D 68, 044026 (2003).
  25. O. Bechmann and O. Lechtenfeld, Classical Quantum Gravity 12, 1473 (1995).
  26. M. Y. Khlopov, B. A. Malomed, I. B. Zeldovich, and Y. B. Zeldovich, Mon. Not. R. Astron. Soc. 215, 575 (1985).
  27. B. Kleihaus, J. Kunz, E. Radu, and B. Subagyo, Phys. Lett. B 725, 489 (2013).
  28. X. Y. Chew and K. G. Lim, Universe 10, 212 (2024).
  29. R. A. Leese, M. Peyrard, and W. J. Zakrzewski, Nonlinearity 3, 773 (1990).
  30. P. Salmi and P. Sutcliffe, J. Phys. A 48, 035401 (2015).
  31. A. Samoilenka and Y. Shnir, Phys. Rev. D 93, 065018 (2016).
  32. M. Gillard, D. Harland, and M. Speight, Nucl. Phys. B895, 272 (2015).
  33. A. A. Starobinsky, Phys. Lett. 91B, 99 (1980).
  34. J. Kunz and Y. Shnir, Phys. Rev. D 107, 104062 (2023).
  35. C. Herdeiro, E. Radu, and Y. Shnir, Phys. Lett. B 856, 138912 (2024).
  36. J. Kunz, V. Loiko, and Y. Shnir, Phys. Rev. D 110, 125020 (2024).
  37. C. A. R. Herdeiro, J. Kunz, I. Perapechka, E. Radu, and Y. Shnir, Phys. Rev. D 103, 065009 (2021).
  38. S. Stotyn, M. Chanona, and R. B. Mann, Phys. Rev. D 89, 044018 (2014).
  39. W. Schönauer and R. Weiß, J. Comput. Appl. Math. 27, 279 (1989); M. Schauder, R. Weiß, and W. Schönauer, The cadsol Program Package Universität Karlsruhe, 1992, Interner Bericht Nr. 46/92.
  40. N. I. M. Gould, J. A. Scout, and Y. Hu, ACM Trans. Math. Softw. 33, 10 (2007).
  41. J. Kunz, I. Perapechka, and Y. Shnir, J. High Energy Phys. 07 (2019) 109.
  42. C. Herdeiro, I. Perapechka, E. Radu, and Y. Shnir, Phys. Lett. B 824, 136811 (2022).
  43. A. Mikhaliuk and Y. Shnir, Phys. Rev. D 112, 025015 (2025).
  44. P. Jetzer, Phys. Lett. B 231, 433 (1989).
  45. P. Jetzer, P. Liljenberg, and B. S. Skagerstam, Astropart. Phys. 1, 429 (1993).
  46. D. Pugliese, H. Quevedo, J. A. Rueda H., and R. Ruffini, Phys. Rev. D 88, 024053 (2013).
  47. B. Kleihaus, J. Kunz, C. Lämmerzahl, and M. List, Phys. Lett. B 675, 102 (2009).
  48. S. Kumar, U. Kulshreshtha, and D. Shankar Kulshreshtha, Classical Quantum Gravity 31, 167001 (2014).
  49. C. A. R. Herdeiro, J. Kunz, I. Perapechka, E. Radu, and Y. Shnir, Phys. Lett. B 812, 136027 (2021).
  50. C. A. R. Herdeiro and E. Radu, Phys. Rev. Lett. 112, 221101 (2014).
  51. B. Kleihaus, J. Kunz, and S. Yazadjiev, Phys. Lett. B 744, 406 (2015).
  52. C. A. R. Herdeiro and E. Radu, Int. J. Mod. Phys. D 24, 1542014 (2015).

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Phys. Rev. D 113, 025009– Published 21 January, 2026
  • Received 20 August 2025
  • Accepted 24 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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