- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Superrenormalizable hairy meronic black holes

Luis Avilés1,2,* and Borja Diez3,†

  • 1Instituto de Ciencias Exactas y Naturales, Universidad Arturo Prat, Playa Brava 3256, 1111346, Iquique, Chile
  • 2Facultad de Ciencias, Universidad Arturo Prat, Avenida Arturo Prat Chacón 2120, 1110939, Iquique, Chile
  • 3Departamento de Física, Cinvestav, Av. IPN 2508, 07360, CDMX, México

  • *Contact author: luaviles@unap.cl
  • †Contact author: borja.diez@cinvestav.mx
PDF

Phys. Rev. D 114, 024010 – Published 6 July, 2026

DOI: https://doi.org/10.1103/x32x-tjrz

Abstract

We construct an analytical black hole solution in the Einstein-Maxwell-Yang-Mills theory with a conformally coupled scalar field in four dimensions, which generalizes the charged Martínez-Troncoso-Zanelli (MTZ) black hole in the presence of self-gravitating non-Abelian gauge fields. The internal gauge group is determined by the horizon curvature, becoming SU(N) in the case of positive curvature and SU(N−1,1) when the curvature is negative. Moreover, this solution is employed as a conformal seed to obtain new meronic spacetimes dressed with all superrenormalizable contributions of the scalar field, which provides the generalization of the Anabalón-Cisterna solution when self–gravitating non-Abelian gauge fields are included. Finally, we consider the non-Noetherian extension of the conformal scalar fields, which still yields a second-order conformally invariant scalar equation, even though the action is not. In that case, we show that static black hole solutions can also be charged with Yang-Mills fields.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (125)

  1. P. Bizon, Phys. Rev. Lett. 64, 2844 (1990).
  2. J. A. Smoller and A. G. Wasserman, J. Math. Phys. (N.Y.) 38, 6522 (1997).
  3. E. Winstanley, Lect. Notes Phys. 769, 49 (2009).
  4. M. S. Volkov and D. V. Gal’tsov, Phys. Rep. 319, 1 (1999).
  5. R. Bartnik and J. Mckinnon, Phys. Rev. Lett. 61, 141 (1988).
  6. B. L. Shepherd and E. Winstanley, Phys. Rev. D 93, 064064 (2016).
  7. B. L. Shepherd and E. Winstanley, J. High Energy Phys. 01 (2017) 065.
  8. V. de Alfaro, S. Fubini, and G. Furlan, Phys. Lett. B 65, 163 (1976).
  9. B. Diez and L. Guajardo, arXiv:2604.14046.
  10. C. G. Callan, Jr., R. F. Dashen, and D. J. Gross, Phys. Lett. B 66, 375 (1977).
  11. C. G. Callan, Jr., R. F. Dashen, and D. J. Gross, Phys. Rev. D 17, 2717 (1978).
  12. C. G. Callan, Jr., R. F. Dashen, and D. J. Gross, Phys. Rev. D 19, 1826 (1979).
  13. J. W. Negele, Nucl. Phys. B, Proc. Suppl. 73, 92 (1999).
  14. J. V. Steele and J. W. Negele, Phys. Rev. Lett. 85, 4207 (2000).
  15. A. M. Polyakov, Nucl. Phys. B120, 429 (1977).
  16. A. Actor, Rev. Mod. Phys. 51, 461 (1979).
  17. F. Canfora, F. Correa, A. Giacomini, and J. Oliva, Phys. Lett. B 722, 364 (2013).
  18. F. Canfora, S. H. Oh, and P. Salgado-Rebolledo, Phys. Rev. D 96, 084038 (2017).
  19. F. Canfora, A. Gomberoff, S. H. Oh, F. Rojas, and P. Salgado-Rebolledo, J. High Energy Phys. 06 (2019) 081.
  20. F. Canfora, A. Gomberoff, M. Lagos, and A. Vera, Phys. Rev. D 105, 084045 (2022).
  21. D. Flores-Alfonso and B. O. Larios, Phys. Rev. D 102, 064017 (2020).
  22. F. Canfora and P. Salgado-Rebolledo, Phys. Rev. D 87, 045023 (2013).
  23. F. Canfora and H. Maeda, Phys. Rev. D 87, 084049 (2013).
  24. F. Canfora, Phys. Rev. D 88, 065028 (2013).
  25. S. Chen, Y.-X. Li, and Y. Yang, Phys. Rev. D 89, 025007 (2014).
  26. F. Canfora, F. Correa, and J. Zanelli, Phys. Rev. D 90, 085002 (2014).
  27. F. Canfora, A. Giacomini, and S. A. Pavluchenko, Phys. Rev. D 90, 043516 (2014).
  28. F. Canfora and G. Tallarita, J. High Energy Phys. 09 (2014) 136.
  29. F. Canfora, M. Di Mauro, M. A. Kurkov, and A. Naddeo, Eur. Phys. J. C 75, 443 (2015).
  30. S. Chen and Y. Yang, Nucl. Phys. B904, 470 (2016).
  31. E. Ayón-Beato, F. Canfora, and J. Zanelli, Phys. Lett. B 752, 201 (2016).
  32. F. Canfora and G. Tallarita, Phys. Rev. D 91, 085033 (2015).
  33. F. Canfora and G. Tallarita, Phys. Rev. D 94, 025037 (2016).
  34. G. Tallarita and F. Canfora, Nucl. Phys. B921, 394 (2017).
  35. F. Canfora, A. Paliathanasis, T. Taves, and J. Zanelli, Phys. Rev. D 95, 065032 (2017).
  36. F. Canfora, N. Dimakis, and A. Paliathanasis, Phys. Rev. D 96, 025021 (2017).
  37. F. Canfora, S. H. Oh, and P. Salgado-Rebolledo, Phys. Rev. D 96, 084038 (2017).
  38. F. Canfora, C. Corral, and B. Diez, Phys. Rev. D 111, 084072 (2025).
  39. M. Ipinza and P. Salgado-Rebolledo, Eur. Phys. J. C 81, 654 (2021).
  40. S. Bahamonde, arXiv:2604.15758.
  41. C. A. R. Herdeiro and E. Radu, Int. J. Mod. Phys. D 24, 1542014 (2015).
  42. J. D. Bekenstein, Ann. Phys. (N.Y.) 82, 535 (1974).
  43. C. Martinez, R. Troncoso, and J. Zanelli, Phys. Rev. D 67, 024008 (2003).
  44. C. Martinez, J. P. Staforelli, and R. Troncoso, Phys. Rev. D 74, 044028 (2006).
  45. C. Charmousis, T. Kolyvaris, and E. Papantonopoulos, Classical Quantum Gravity 26, 175012 (2009).
  46. Y. Bardoux, M. M. Caldarelli, and C. Charmousis, J. High Energy Phys. 05 (2014) 039.
  47. M. Astorino, Phys. Rev. D 91, 064066 (2015).
  48. A. Anabalon and H. Maeda, Phys. Rev. D 81, 041501 (2010).
  49. A. Cisterna, A. Neira-Gallegos, J. Oliva, and S. C. Rebolledo-Caceres, Phys. Rev. D 103, 064050 (2021).
  50. N. Caceres, J. Figueroa, J. Oliva, M. Oyarzo, and R. Stuardo, J. High Energy Phys. 04 (2020) 157.
  51. J. Barrientos, A. Cisterna, N. Mora, and A. Viganò, Phys. Rev. D 106, 024038 (2022).
  52. L. Avilés, H. Maeda, and C. Martinez, Classical Quantum Gravity 35, 245001 (2018).
  53. A. Cisterna, K. Müller, K. Pallikaris, and A. Viganò, Phys. Rev. D 108, 024066 (2023).
  54. M. Bravo-Gaete, F. F. Santos, J. A. Herrera-Mendoza, and D. F. Higuita-Borja, Classical Quantum Gravity 43, 075011 (2026).
  55. J. Barrientos and A. Cisterna, Phys. Rev. D 108, 024059 (2023).
  56. E. Arratia, C. Corral, J. Figueroa, and L. Sanhueza, Phys. Rev. D 103, 064068 (2021).
  57. C. Corral, B. Diez, and E. Papantonopoulos, arXiv:2510.11854.
  58. S. de Haro, I. Papadimitriou, and A. C. Petkou, Phys. Rev. Lett. 98, 231601 (2007).
  59. N. M. Bocharova, K. A. Bronnikov, and V. N. Melnikov, Vestn. Mosk. Univ., Ser. 3: Fiz., Astron. 6, 706 (1970).
  60. D. Sudarsky and T. Zannias, Phys. Rev. D 58, 087502 (1998).
  61. M. Astorino, Phys. Rev. D 89, 044022 (2014).
  62. G. Anastasiou, I. J. Araya, M. Busnego-Barrientos, C. Corral, and N. Merino, Phys. Rev. D 107, 104049 (2023).
  63. B. C. Xanthopoulos and T. E. Dialynas, J. Math. Phys. (N.Y.) 33, 1463 (1992).
  64. C. Klimcik, J. Math. Phys. (N.Y.) 34, 1914 (1993).
  65. J. Oliva and S. Ray, Classical Quantum Gravity 29, 205008 (2012).
  66. G. Giribet, M. Leoni, J. Oliva, and S. Ray, Phys. Rev. D 89, 085040 (2014).
  67. M. Chernicoff, M. Galante, G. Giribet, A. Goya, M. Leoni, J. Oliva, and G. Perez-Nadal, J. High Energy Phys. 06 (2016) 159.
  68. E. Babichev, C. Charmousis, M. Hassaine, and N. Lecoeur, Phys. Rev. D 107, 084050 (2023).
  69. E. Ayon-Beato, C. Martinez, and J. Zanelli, Gen. Relativ. Gravit. 38, 145 (2006).
  70. E. Ayon-Beato, C. Martinez, R. Troncoso, and J. Zanelli, Phys. Rev. D 71, 104037 (2005).
  71. A. Anabalon and A. Cisterna, Phys. Rev. D 85, 084035 (2012).
  72. L. Zhao, W. Xu, and B. Zhu, Commun. Theor. Phys. 61, 475 (2014).
  73. W. Xu, L. Zhao, and D.-C. Zou, arXiv:1406.7153.
  74. E. Ayón-Beato, M. Hassaïne, and J. A. Méndez-Zavaleta, Phys. Rev. D 92, 024048 (2015); 96, 049905(A) (2017).
  75. Z.-Y. Fan and H. Lu, Phys. Rev. D 92, 064008 (2015).
  76. C. Erices and C. Martinez, Phys. Rev. D 97, 024034 (2018).
  77. E. Ayon-Beato and M. Hassaine, Phys. Rev. D 71, 084004 (2005).
  78. E. Ayón-Beato, P. I. Ramírez-Baca, and C. A. Terrero-Escalante, Phys. Rev. D 97, 043505 (2018).
  79. C. Erices, L. Guajardo, and K. Lara, J. Cosmol. Astropart. Phys. 03 (2025) 051.
  80. P. G. S. Fernandes, Phys. Rev. D 103, 104065 (2021).
  81. E. Ayón-Beato and M. Hassaine, Ann. Phys. (N.Y.) 460, 169567 (2024).
  82. E. Ayón-Beato, D. Flores-Alfonso, and M. Hassaine, Phys. Rev. D 110, 064027 (2024).
  83. S. Bertini, S. L. Cacciatori, and B. L. Cerchiai, J. Math. Phys. (N.Y.) 47, 043510 (2006).
  84. S. L. Cacciatori, F. Dalla Piazza, and A. Scotti, Trans. Am. Math. Soc. 369, 4709 (2017).
  85. T. E. Tilma and G. Sudarshan, J. Geom. Phys. 52, 263 (2004).
  86. C. Corral, D. Flores-Alfonso, G. Giribet, and J. Oliva, Eur. Phys. J. C 84, 959 (2024).
  87. E. A. Bergshoeff, O. Hohm, and P. K. Townsend, Phys. Rev. Lett. 102, 201301 (2009).
  88. F. Canfora and C. Corral, J. High Energy Phys. 11 (2023) 146.
  89. E. Ayón-Beato, F. Canfora, M. Lagos, J. Oliva, and A. Vera, Eur. Phys. J. C 80, 384 (2020).
  90. G. Barriga, C. Henríquez-Báez, L. Sanhueza, and A. Vera, arXiv:2511.11382.
  91. A. Vera, J. High Energy Phys. 10 (2025) 119.
  92. C. Henríquez-Baez, M. Lagos, E. Rodríguez, and A. Vera, Phys. Rev. D 111, 104016 (2025).
  93. P. Concha, C. Henríquez-Baez, E. Rodríguez, and A. Vera, Phys. Rev. D 107, 124043 (2023).
  94. C. Henríquez-Báez, M. Lagos, and A. Vera, Phys. Rev. D 106, 064027 (2022).
  95. D. Flores-Alfonso, Phys. Rev. D 111, 124014 (2025).
  96. S. L. Cacciatori, F. Canfora, M. Lagos, F. Muscolino, and A. Vera, J. High Energy Phys. 12 (2021) 150.
  97. P. D. Alvarez, S. L. Cacciatori, F. Canfora, and B. L. Cerchiai, Phys. Rev. D 101, 125011 (2020).
  98. S. L. Cacciatori, F. Canfora, M. Lagos, F. Muscolino, and A. Vera, Nucl. Phys. B976, 115693 (2022).
  99. A.-M. Barlow, D. Doherty, and E. Winstanley, Phys. Rev. D 72, 024008 (2005).
  100. T. J. T. Harper, P. A. Thomas, E. Winstanley, and P. M. Young, Phys. Rev. D 70, 064023 (2004).
  101. M. Salgado, Classical Quantum Gravity 20, 4551 (2003).
  102. A. Ashtekar, A. Corichi, and D. Sudarsky, Classical Quantum Gravity 20, 3413 (2003).
  103. A. Ashtekar and A. Corichi, Classical Quantum Gravity 20, 4473 (2003).
  104. P. L. McFadden and N. G. Turok, Phys. Rev. D 71, 086004 (2005).
  105. M. Salgado, Classical Quantum Gravity 23, 4719 (2006).
  106. R. Jackiw, Theor. Math. Phys. 148, 941 (2006).
  107. E. Ayón-Beato and M. Hassaine, Ann. Phys. (Amsterdam) 458, 169446 (2023).
  108. E. Babichev, C. Charmousis, M. Hassaine, and N. Lecoeur, Phys. Rev. D 106, 064039 (2022).
  109. E. Ayón-Beato, M. Hassaine, and P. A. Sánchez, Eur. Phys. J. C 85, 259 (2025).
  110. P. A. Sánchez, Phys. Rev. D 111, 084010 (2025).
  111. U. Hernandez-Vera, Phys. Rev. D 111, 084035 (2025).
  112. P. G. S. Fernandes, P. Carrilho, T. Clifton, and D. J. Mulryne, Classical Quantum Gravity 39, 063001 (2022).
  113. G. W. Horndeski, Int. J. Theor. Phys. 10, 363 (1974).
  114. E. Babichev, C. Charmousis, M. Hassaine, and N. Lecoeur, Phys. Rev. D 108, 024019 (2023).
  115. D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020).
  116. H. Lu and Y. Pang, Phys. Lett. B 809, 135717 (2020).
  117. P. G. S. Fernandes, P. Carrilho, T. Clifton, and D. J. Mulryne, Phys. Rev. D 102, 024025 (2020).
  118. R. A. Hennigar, D. Kubizňák, R. B. Mann, and C. Pollack, J. High Energy Phys. 07 (2020) 027.
  119. P. G. S. Fernandes, P. Carrilho, T. Clifton, and D. J. Mulryne, Phys. Rev. D 104, 044029 (2021).
  120. P. G. S. Fernandes, Phys. Lett. B 805, 135468 (2020).
  121. M. Hassaine, U. Hernandez-Vera, and F. Lara-Munoz, Phys. Rev. D 108, 104067 (2023).
  122. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, Phys. Rev. D 102, 121703 (2020).
  123. F. Canfora, C. Corral, B. Diez, L. Guajardo, and J. Oliva, arXiv:2511.15437.
  124. D. J. Cirilo-Lombardo, Int. J. Geom. Methods Mod. Phys. 20, 2350238 (2023).
  125. L. Avilés, C. Corral, F. Izaurieta, O. Valdivia, and C. Vera, Phys. Rev. D 109, 084039 (2024).

Outline

Information

Phys. Rev. D 114, 024010– Published 6 July, 2026
  • Received 5 May 2026
  • Accepted 2 June 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation