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Perturbations in the parametrized wormhole spacetime and their related quasinormal modes

Shauvik Biswas* and Sayan Chakrabarti†

  • *Contact author: shauvikbiswas2014@gmail.com
  • †Contact author: sayan.chakrabarti@iitg.ac.in
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Phys. Rev. D 114, 084055 – Published 20 October, 2026

DOI: https://doi.org/10.1103/hzbj-xjfc

Abstract

We study electromagnetic perturbations and the associated quasinormal modes (QNMs) of parametrized static, spherically symmetric wormhole spacetimes, focusing on Damour-Solodukhin and braneworld geometries as well as their galactic extensions. Using the Bronnikov-Konoplya-Pappas (BKP) parametrization, we express the metric functions in terms of a compactified radial coordinate and characterize the spacetime through far-field and near-throat parameters. The far-field coefficients govern the asymptotic structure and post-Newtonian behavior, while the near-throat continued-fraction expansion captures the strong-field geometry near the throat. We first apply the parametrization to isolated wormholes and identify its range of validity, showing that the nonanalytic metric functions can limit the applicability of the BKP scheme. Moreover we have shown that such issues can indeed hamper the primary ringdown waveform. We then extend the framework to a galactic Damour-Solodukhin wormhole embedded in a Hernquist dark matter halo. Imposing observational bounds from the shadow of Sgr A*, we constrain the galactic compactness and deformation parameters and obtain an observationally viable parametrized metric. Within the allowed parameter space, we compute the fundamental QNM frequencies using the transfer matrix method and analyze the corresponding time-domain ringdown signals. We find that the damping rate is more sensitive to galactic compactness, whereas the oscillation frequency remains comparatively stable. Although the spectral shifts are small within the shadow-allowed region, the framework provides a systematic link between geometric parametrization, shadow constraints, and dynamical response. Our results establish an observationally consistent parametrized description of wormhole perturbations for strong-field tests of horizonless compact objects.

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References (59)

  1. E. Berti et al., Testing general relativity with present and future astrophysical observations, Classical Quantum Gravity 32 (2015) 243001,
  2. V. Cardoso, S. Biswas, and S. Sarkar, The physics of black holes and their environments: Consequences for gravitational wave science, arXiv:2511.14841.
  3. V. Cardoso and P. Pani, Testing the nature of dark compact objects: A status report, Living Rev. Relativity 22, 4 (2019).
  4. M. Visser, Lorentzian Wormholes: From Einstein to Hawking (American Institute of Physics Melville, New York, 1996).
  5. A. Einstein and N. Rosen, The particle problem in the general theory of relativity, Phys. Rev. 48, 73 (1935).
  6. M. S. Morris and K. S. Thorne, Wormholes in space-time and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56, 395 (1988).
  7. F. S. N. Lobo and M. A. Oliveira, Wormhole geometries in f(R) modified theories of gravity, Phys. Rev. D 80, 104012 (2009).
  8. T. Harko, F. S. N. Lobo, M. K. Mak, and S. V. Sushkov, Modified-gravity wormholes without exotic matter, Phys. Rev. D 87, 067504 (2013).
  9. J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortschr. Phys. 61, 781 (2013).
  10. A. R. Brown, H. Gharibyan, S. Leichenauer, H. W. Lin, S. Nezami, G. Salton, L. Susskind, B. Swingle, and M. Walter, Quantum gravity in the lab. I. Teleportation by size and traversable wormholes, PRX Quantum 4, 010320 (2023).
  11. G. Sen, D. Maity, and S. Das, Study of relativistic hot accretion flow around Kerr-like wormhole, J. Cosmol. Astropart. Phys. 10 (2024) 068.
  12. S. Kumar, A. Uniyal, and S. Chakrabarti, Shadow and weak gravitational lensing of rotating traversable wormhole in nonhomogeneous plasma spacetime, Phys. Rev. D 109, 104012 (2024).
  13. S. Kumar, A. Uniyal, and S. Chakrabarti, Observational signatures of rotating compact objects in Plasma space–time, Phys. Dark Universe 44, 101472 (2024).
  14. S. Biswas, Can wormholes have vanishing Love numbers?, Phys. Rev. D 114, 064050 (2026).
  15. V. Cardoso, S. Hopper, C. F. B. Macedo, C. Palenzuela, and P. Pani, Gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale, Phys. Rev. D 94, 084031 (2016).
  16. Z. Mark, A. Zimmerman, S. M. Du, and Y. Chen, A recipe for echoes from exotic compact objects, Phys. Rev. D 96, 084002 (2017).
  17. J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortschr. Phys. 61, 781 (2013).
  18. J. C. Baez and J. Vicary, Wormholes and entanglement, Classical Quantum Gravity 31, 214007 (2014).
  19. V. Cardoso, E. Franzin, and P. Pani, Is the gravitational-wave ringdown a probe of the event horizon?, Phys. Rev. Lett. 116, 171101 (2016); 117, 089902(E) (2016).
  20. K. A. Bronnikov and S. Grinyok, Instability of wormholes with a nonminimally coupled scalar field, Gravitation Cosmol. 7, 297 (2001), arXiv:gr-qc/0201083.
  21. K. A. Bronnikov, R. A. Konoplya, and A. Zhidenko, Instabilities of wormholes and regular black holes supported by a phantom scalar field, Phys. Rev. D 86, 024028 (2012).
  22. J. A. Gonzalez, F. S. Guzman, and O. Sarbach, Instability of wormholes supported by a ghost scalar field. I. Linear stability analysis, Classical Quantum Gravity 26, 015010 (2009).
  23. E. Maggio, V. Cardoso, S. R. Dolan, and P. Pani, Ergoregion instability of exotic compact objects: Electromagnetic and gravitational perturbations and the role of absorption, Phys. Rev. D 99, 064007 (2019).
  24. L. Rezzolla and A. Zhidenko, New parametrization for spherically symmetric black holes in metric theories of gravity, Phys. Rev. D 90, 084009 (2014).
  25. T. Johannsen and D. Psaltis, A metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem, Phys. Rev. D 83, 124015 (2011).
  26. K. A. Bronnikov, R. A. Konoplya, and T. D. Pappas, General parametrization of wormhole spacetimes and its application to shadows and quasinormal modes, Phys. Rev. D 103, 124062 (2021).
  27. E. Berti, V. Cardoso, and A. O. Starinets, Quasinormal modes of black holes and black branes, Classical Quantum Gravity 26, 163001 (2009).
  28. R. A. Konoplya and A. Zhidenko, Quasinormal modes of black holes: From astrophysics to string theory, Rev. Mod. Phys. 83, 793 (2011).
  29. E. Berti et al., Black hole spectroscopy: From theory to experiment, Classical Quantum Gravity 43, 123001 (2026).
  30. F. S. Khoo, B. Azad, J. L. Blázquez-Salcedo, L. M. González-Romero, B. Kleihaus, J. Kunz, and F. Navarro-Lérida, Quasinormal modes of rapidly rotating Ellis-Bronnikov wormholes, Phys. Rev. D 109, 084013 (2024).
  31. S. Aneesh, S. Bose, and S. Kar, Gravitational waves from quasinormal modes of a class of Lorentzian wormholes, Phys. Rev. D 97, 124004 (2018).
  32. K. Akiyama et al. (Event Horizon Telescope Collaboration), First M87 event horizon telescope results. I. The shadow of the supermassive black hole, Astrophys. J. Lett. 875, L1 (2019).
  33. P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, Eht constraint on the ultralight scalar hair of the M87 supermassive black hole, Universe 5, 220 (2019).
  34. M. Afrin and S. G. Ghosh, Tests of loop quantum gravity from the event horizon telescope results of Sgr A*, Astrophys. J. 944, 149 (2023).
  35. K. Akiyama et al. (Event Horizon Telescope Collaboration), First Sagittarius A* event horizon telescope results. VI. Testing the black hole metric, Astrophys. J. Lett. 930, L17 (2022).
  36. S. Vagnozzi, R. Roy, Y.-D. Tsai, L. Visinelli, M. Afrin, A. Allahyari, P. Bambhaniya, D. Dey, S. G. Ghosh, P. S. Joshi, K. Jusufi, M. Khodadi, R. K. Walia, A. Övgün, and C. Bambi, Horizon-scale tests of gravity theories and fundamental physics from the event horizon telescope image of Sagittarius A*, Classical Quantum Gravity 40, 165007 (2023).
  37. M. Khodadi, G. Lambiase, and D. F. Mota, No-hair theorem in the wake of event horizon telescope, J. Cosmol. Astropart. Phys. 09 (2020) 026.
  38. S. Gera, S. Kumar, P. Dutta Roy, and S. Chakrabarti, Shadows of generalised Hayward spacetimes: In vacuum and with plasma, J. Cosmol. Astropart. Phys. 07 (2025) 065.
  39. D. Psaltis, Testing general relativity with the event horizon telescope, Gen. Relativ. Gravit. 51, 137 (2019).
  40. S. Biswas, C. Singha, and S. Chakraborty, Galactic wormholes: Geometry, stability, and echoes, Phys. Rev. D 109, 064043 (2024).
  41. P. Bueno, P. A. Cano, F. Goelen, T. Hertog, and B. Vercnocke, Echoes of Kerr-like wormholes, Phys. Rev. D 97, 024040 (2018).
  42. S. Biswas, M. Rahman, and S. Chakraborty, Echoes from braneworld wormholes, Phys. Rev. D 106, 124003 (2022).
  43. R. K. Karimov, R. N. Izmailov, and K. K. Nandi, Accretion disk around the rotating Damour–Solodukhin wormhole, Eur. Phys. J. C 79, 952 (2019).
  44. S. Maharana, F. Simovic, I. Soranidis, and D. R. Terno, Padé metrics for black hole perturbations and light rings, Phys. Rev. D 111, 104063 (2025).

  45. One should always check this hierarchy for a valid parametrization.

  46. R. A. Konoplya and A. Zhidenko, Quasinormal ringing of general spherically symmetric parametrized black holes, Phys. Rev. D 105, 104032 (2022).
  47. T. Damour and S. N. Solodukhin, Wormholes as black hole foils, Phys. Rev. D 76, 024016 (2007).
  48. S. Kanno and J. Soda, Radion and holographic brane gravity, Phys. Rev. D 66, 083506 (2002).
  49. S. Kar, S. Lahiri, and S. SenGupta, Can extra dimensional effects allow wormholes without exotic matter?, Phys. Lett. B 750, 319 (2015).
  50. S. Aneesh, S. Bose, and S. Kar, Gravitational waves from quasinormal modes of a class of Lorentzian wormholes, Phys. Rev. D 97, 124004 (2018).
  51. A. Ianniccari, A. J. Iovino, A. Kehagias, P. Pani, G. Perna, D. Perrone, and A. Riotto, Deciphering the instability of the black hole ringdown quasinormal spectrum, Phys. Rev. Lett. 133, 211401 (2024).
  52. L. Hernquist, An analytical model for spherical galaxies and bulges, Astrophys. J. 356, 359 (1990).

  53. The reader may argue that γ itself contains transcendental behavior, but since expansion of tan−1(x) has polynomial dependence on x so that one can read-off a1.

  54. S. Vagnozzi et al., Horizon-scale tests of gravity theories and fundamental physics from the event horizon telescope image of Sagittarius A, Classical Quantum Gravity 40, 165007 (2023).
  55. V. Cardoso, A. S. Miranda, E. Berti, H. Witek, and V. T. Zanchin, Geodesic stability, Lyapunov exponents and quasinormal modes, Phys. Rev. D 79, 064016 (2009).
  56. R. F. Rosato, S. Biswas, S. Chakraborty, and P. Pani, Excitation factors for horizonless compact objects: Long-lived modes, echoes, and greybody factors, Phys. Rev. D 113, 084002 (2026).
  57. B. F. Schutz and C. M. Will, Black hole normal modes: A semianalytic approach, Astrophys. J. 291, L33 (1985).
  58. E. Berti and K. D. Kokkotas, Quasinormal modes of Kerr-Newman black holes: Coupling of electromagnetic and gravitational perturbations, Phys. Rev. D 71, 124008 (2005).
  59. S. Iyer, Black-hole normal modes: A WKB approach. II. Schwarzschild black holes, Phys. Rev. D 35, 3632 (1987).

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Phys. Rev. D 114, 084055– Published 20 October, 2026
  • Received 15 May 2026
  • Accepted 30 September 2026
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