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Scalar quasinormal modes of gravastars

Hamza Boumaza

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Phys. Rev. D 112, 044011 – Published 7 August, 2025

DOI: https://doi.org/10.1103/xhpm-7h7v

Abstract

In this study, we present a detailed investigation of gravastars within the framework of scalar-tensor theories, emphasizing both the background and perturbed levels for trivial and nontrivial scalar field. We derive the background equations that govern the equilibrium configurations of gravastars by examining the interaction between matter and the scalar field through a conformal transformation. By selecting two forms of the coupling function, we identify distinct physical characteristics that lead to deviations from the predictions made by general relativity. Our findings indicate that the scalar field significantly influences the compactness parameter. By extending our study to the perturbed level, we demonstrate that quasinormal modes are considerably affected by the presence of the scalar field. We discover new and intriguing quasinormal modes that are absent in general relativity.

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References (70)

  1. B. Abbott et al. (VIRGO and LIGO Scientific Collaborations), Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
  2. K. Akiyama, A. Alberdi, W. Alef, K. Asada, R. Azulay, A.-K. Baczko, D. Ball, M. Baloković, J. Barrett, D. Bintley et al., First m87 event horizon telescope results. V. Physical origin of the asymmetric ring, Astrophys. J. Lett. 875, L5 (2019).
  3. R. Brito, V. Cardoso, C. A. Herdeiro, and E. Radu, Proca stars: Gravitating Bose–Einstein condensates of massive spin 1 particles, Phys. Lett. B 752, 291 (2016).
  4. F. E. Schunck and E. W. Mielke, General relativistic boson stars, Classical Quantum Gravity 20, R301 (2003).
  5. P. O. Mazur and E. Mottola, Gravitational vacuum condensate stars, Proc. Natl. Acad. Sci. U.S.A. 101, 9545 (2004).
  6. P. O. Mazur and E. Mottola, Gravitational condensate stars: An alternative to black holes, Universe 9, 88 (2023).
  7. B. M. Carter, Stable gravastars with generalized exteriors, Classical Quantum Gravity 22, 4551 (2005).
  8. C. B. Chirenti and L. Rezzolla, How to tell a gravastar from a black hole, Classical Quantum Gravity 24, 4191 (2007).
  9. P. Pani, E. Berti, V. Cardoso, Y. Chen, and R. Norte, Gravitational wave signatures of the absence of an event horizon: Nonradial oscillations of a thin-shell gravastar, Phys. Rev. D 80, 124047 (2009).
  10. P. Pani, E. Berti, V. Cardoso, Y. Chen, and R. Norte, Gravitational wave signatures of the absence of an event horizon. II. Extreme mass ratio inspirals in the spacetime of a thin-shell gravastar, Phys. Rev. D 81, 084011 (2010).
  11. Y. Fujii and K.-i. Maeda, The Scalar-Tensor Theory of Gravitation (Cambridge University Press, Cambridge, England, 2003).
  12. E. Berti et al., Testing general relativity with present and future astrophysical observations, Classical Quantum Gravity 32, 243001 (2015).
  13. D. D. Doneva, S. S. Yazadjiev, and K. D. Kokkotas, Stability of topological neutron stars, Phys. Rev. D 102, 044043 (2020).
  14. H. Boumaza, D. Langlois, and K. Noui, Late-time cosmological evolution in degenerate higher-order scalar-tensor models, Phys. Rev. D 102, 024018 (2020).
  15. D. Langlois, Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review, Int. J. Mod. Phys. D 28, 1942006 (2019).
  16. D. Langlois, R. Saito, D. Yamauchi, and K. Noui, Scalar-tensor theories and modified gravity in the wake of GW170817, Phys. Rev. D 97, 061501 (2018).
  17. J. Ben Achour, H. Liu, and S. Mukohyama, Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method, J. Cosmol. Astropart. Phys. 02 (2020) 023.
  18. M. Minamitsuji and J. Edholm, Black hole solutions in shift-symmetric degenerate higher-order scalar-tensor theories, Phys. Rev. D 100, 044053 (2019).
  19. H. Motohashi and M. Minamitsuji, Exact black hole solutions in shift-symmetric quadratic degenerate higher-order scalar-tensor theories, Phys. Rev. D 99, 064040 (2019).
  20. H. Boumaza, Slowly rotating neutron stars in scalar torsion theory, Eur. Phys. J. C 81, 448 (2021).
  21. H. Ogawa, T. Kobayashi, and K. Koyama, Relativistic stars in a cubic Galileon Universe, Phys. Rev. D 101, 024026 (2020).
  22. H. Boumaza and D. Langlois, Neutron stars in degenerate higher-order scalar-tensor theories, Phys. Rev. D 106, 084053 (2022).
  23. E. Babichev, K. Koyama, D. Langlois, R. Saito, and J. Sakstein, Relativistic stars in beyond Horndeski theories, Classical Quantum Gravity 33, 235014 (2016).
  24. H. Boumaza, Axial perturbations of neutron stars with shift symmetric conformal coupling, Phys. Rev. D 105, 044052 (2022).
  25. A. Cisterna, T. Delsate, and M. Rinaldi, Neutron stars in general second order scalar-tensor theory: The case of nonminimal derivative coupling, Phys. Rev. D 92, 044050 (2015).
  26. A. Cisterna, T. Delsate, L. Ducobu, and M. Rinaldi, Slowly rotating neutron stars in the nonminimal derivative coupling sector of Horndeski gravity, Phys. Rev. D 93, 084046 (2016).
  27. T. Damour and G. Esposito-Farese, Tensor—scalar gravity and binary pulsar experiments, Phys. Rev. D 54, 1474 (1996).
  28. H. O. Silva, J. Sakstein, L. Gualtieri, T. P. Sotiriou, and E. Berti, Spontaneous scalarization of black holes and compact stars from a Gauss-Bonnet coupling, Phys. Rev. Lett. 120, 131104 (2018).
  29. D. D. Doneva, F. M. Ramazanoğlu, H. O. Silva, T. P. Sotiriou, and S. S. Yazadjiev, Spontaneous scalarization, Rev. Mod. Phys. 96, 015004 (2024).
  30. R. F. Mendes and N. Ortiz, Highly compact neutron stars in scalar-tensor theories of gravity: Spontaneous scalarization versus gravitational collapse, Phys. Rev. D 93, 124035 (2016).
  31. M. Minamitsuji and S. Tsujikawa, Spontaneous scalarization of charged stars, Phys. Lett. B 820, 136509 (2021).
  32. H. Boumaza, Axial and polar stability of neutron stars in scalar-tensor theories with disformal coupling, Phys. Rev. D 108, 044068 (2023).
  33. P. Pani and E. Berti, Slowly rotating neutron stars in scalar-tensor theories, Phys. Rev. D 90, 024025 (2014).
  34. H.-J. Kuan, D. D. Doneva, and S. S. Yazadjiev, Dynamical formation of scalarized black holes and neutron stars through stellar core collapse, Phys. Rev. Lett. 127, 161103 (2021).
  35. S. S. Yazadjiev, D. D. Doneva, and D. Popchev, Slowly rotating neutron stars in scalar-tensor theories with a massive scalar field, Phys. Rev. D 93, 084038 (2016).
  36. D. D. Doneva and S. S. Yazadjiev, Neutron star solutions with curvature induced scalarization in the extended Gauss-Bonnet scalar-tensor theories, J. Cosmol. Astropart. Phys. 04 (2018) 011.
  37. N. Andreou, N. Franchini, G. Ventagli, and T. P. Sotiriou, Spontaneous scalarization in generalized scalar-tensor theory, Phys. Rev. D 99, 124022 (2019).
  38. J. D. Bekenstein, The relation between physical and gravitational geometry, Phys. Rev. D 48, 3641 (1993).
  39. O. Benhar, E. Berti, and V. Ferrari, The imprint of the equation of state on the axial w-modes of oscillating neutron stars, Mon. Not. R. Astron. Soc. 310, 797 (1999).
  40. K. D. Kokkotas and B. G. Schmidt, Quasi-normal modes of stars and black holes, Living Rev. Relativity 2, 1 (1999).
  41. K. D. Kokkotas and B. F. Schutz, W-modes: A new family of normal modes of pulsating relativistic stars, Mon. Not. R. Astron. Soc. 255, 119 (1992).
  42. Z. A. Motahar, J. L. Blázquez-Salcedo, D. D. Doneva, J. Kunz, and S. S. Yazadjiev, Axial quasinormal modes of scalarized neutron stars with massive self-interacting scalar field, Phys. Rev. D 99, 104006 (2019).
  43. W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cimento B 44S10, 1 (1966); 48, 463(E) (1967).
  44. T. Damour and G. Esposito-Farese, Nonperturbative strong field effects in tensor—scalar theories of gravitation, Phys. Rev. Lett. 70, 2220 (1993).
  45. B. F. Schutz Jr, Perfect fluids in general relativity: Velocity potentials and a variational principle, Phys. Rev. D 2, 2762 (1970).
  46. B. F. Schutz and R. Sorkin, Variational aspects of relativistic field theories, with application to perfect fluids, Ann. Phys. (N.Y.) 107, 1 (1977).
  47. B. Bertotti, L. Iess, and P. Tortora, A test of general relativity using radio links with the Cassini spacecraft, Nature (London) 425, 374 (2003).
  48. T. Damour and A. Nagar, Relativistic tidal properties of neutron stars, Phys. Rev. D 80, 084035 (2009).
  49. T. Damour and G. Esposito-Farese, Nonperturbative strong-field effects in tensor-scalar theories of gravitation, Phys. Rev. Lett. 70, 2220 (1993).
  50. R. F. P. Mendes and N. Ortiz, Highly compact neutron stars in scalar-tensor theories of gravity: Spontaneous scalarization versus gravitational collapse, Phys. Rev. D 93, 124035 (2016).
  51. E. Berti, E. Barausse, V. Cardoso, L. Gualtieri, P. Pani, U. Sperhake, L. C. Stein, N. Wex, K. Yagi, T. Baker et al., Testing general relativity with present and future astrophysical observations, Classical Quantum Gravity 32, 243001 (2015).
  52. D. D. Doneva, F. M. Ramazanoğlu, H. O. Silva, T. P. Sotiriou, and S. S. Yazadjiev, Spontaneous scalarization, Rev. Mod. Phys. 96, 015004 (2024).
  53. A. G. S. Landulfo, W. C. C. Lima, G. E. A. Matsas, and D. A. T. Vanzella, From quantum to classical instability in relativistic stars, Phys. Rev. D 91, 024011 (2015).
  54. A. De Felice, T. Suyama, and T. Tanaka, Stability of Schwarzschild-like solutions in f(R,G) gravity models, Phys. Rev. D 83, 104035 (2011).
  55. T. Kobayashi, H. Motohashi, and T. Suyama, Black hole perturbation in the most general scalar-tensor theory with second-order field equations II: The even-parity sector, Phys. Rev. D 89, 084042 (2014).
  56. R. Kase, R. Kimura, S. Sato, and S. Tsujikawa, Stability of relativistic stars with scalar hairs, Phys. Rev. D 102, 084037 (2020).
  57. M. Minamitsuji and H. O. Silva, Relativistic stars in scalar-tensor theories with disformal coupling, Phys. Rev. D 93, 124041 (2016).
  58. M. Leins, H.-P. Nollert, and M. Soffel, Nonradial oscillations of neutron stars: A new branch of strongly damped normal modes, Phys. Rev. D 48, 3467 (1993).
  59. E. W. Leaver, Quasinormal modes of Reissner-Nordström black holes, Phys. Rev. D 41, 2986 (1990).
  60. H. Roussille, D. Langlois, and K. Noui, Numerical computation of quasinormal modes in the first-order approach to black hole perturbations in modified gravity, J. Cosmol. Astropart. Phys. 01 (2024) 054.
  61. P. Pani, E. Berti, V. Cardoso, Y. Chen, and R. Norte, Gravitational wave signatures of the absence of an event horizon. I. Nonradial oscillations of a thin-shell gravastar, Phys. Rev. D 80, 124047 (2009).
  62. P. Pani, E. Berti, V. Cardoso, Y. Chen, and R. Norte, Gravitational-wave signatures of the absence of an event horizon. II. Extreme mass ratio inspirals in the spacetime of a thin-shell gravastar, Phys. Rev. D 81, 084011 (2010).
  63. T. R. Choudhury and T. Padmanabhan, Quasinormal modes in Schwarzschild–de Sitter spacetime: A simple derivation of the level spacing of the frequencies, Phys. Rev. D 69, 064033 (2004).
  64. H.-P. Nollert, Quasinormal modes: The characteristicsound’of black holes and neutron stars, Classical Quantum Gravity 16, R159 (1999).
  65. S. Hod, Bohr’s correspondence principle and the area spectrum of quantum black holes, Phys. Rev. Lett. 81, 4293 (1998).
  66. L. Motl and A. Neitzke, Asymptotic black hole quasinormal frequencies, Adv. Theor. Math. Phys. 7, 307 (2003).
  67. M. Maggiore, Black holes as quantum membranes, Nucl. Phys. B429, 205 (1994).
  68. M. Maggiore, Physical interpretation of the spectrum of black hole quasinormal modes, Phys. Rev. Lett. 100, 141301 (2008).
  69. C. Corda, Effective temperature, Hawking radiation and quasinormal modes, Int. J. Mod. Phys. D 21, 1242023 (2012).
  70. C. Corda, S. Hendi, R. Katebi, and N. Schmidt, Effective state, Hawking radiation and quasi-normal modes for Kerr black holes, J. High Energy Phys. 06 (2013) 008.

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Phys. Rev. D 112, 044011– Published 7 August, 2025
  • Received 28 April 2025
  • Accepted 24 July 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.

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