- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

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
  • Access by Xinjiang University

Tidal gap: Causality bound on exotic compact objects

Benedetta Russo1,* and Alfredo Urbano1,2,†

  • *Contact author: russo.1914359@studenti.uniroma1.it
  • †Contact author: alfredo.urbano@uniroma1.it
PDF

Phys. Rev. D 114, 104007 – Published 3 November, 2026

DOI: https://doi.org/10.1103/wsc5-m2w6

Abstract

In this work, we highlight the existence of a lower limit on the tidal deformability parameter Λ for static, isotropic compact objects. Additionally, by considering the corresponding upper bound on compactness, we identify the region within the compactness–tidal-deformability parameter space where physically motivated exotic compact objects could potentially reside. Our analysis reveals the presence of a “tidal gap” between black holes, characterized by vanishing tidal deformability, and horizonless compact objects. Prompted by this finding, we investigate the possibility that a population of maximally compact exotic objects described by a linear equation of state may simultaneously inhabit the lower-mass gap and the subsolar region, thus qualifying as (primordial) black hole mimickers while distinguishing themselves from the latter through their nonzero tidal deformability. We also provide an illustrative estimate of the prospects for probing their tidal response with present and future gravitational-wave detectors. Finally, considering solitonic boson stars as explicit field-theoretical exotic compact objects whose bulk structure approximately reproduces the linear equation of state, we show that values of Λ below the isotropic limit can be reached without violating relativistic causality. This result reflects the relaxation of the isotropic perfect-fluid and sharp-surface assumptions: the dominant energy condition remains satisfied, whereas the strong energy condition is locally violated near the effective surface.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (28)

  1. H. A. Buchdahl, Phys. Rev. 116, 1027 (1959).
  2. L. Lindblom, Astrophys. J. 278, 364 (1984).
  3. N. K. Glendenning, Phys. Rev. D 46, 4161 (1992).
  4. J. M. Lattimer and M. Prakash, Phys. Rep. 442, 109 (2007).
  5. A. Urbano and H. Veermäe, J. Cosmol. Astropart. Phys. 04 (2019) 011.
  6. K. S. Thorne, Rev. Mod. Phys. 52, 299 (1980).
  7. K. Yagi and N. Yunes, Phys. Rev. D 88, 023009 (2013).
  8. P. Charalambous, S. Dubovsky, and M. M. Ivanov, J. High Energy Phys. 10 (2022) 175.
  9. O. Combaluzier-Szteinsznaider, L. Hui, L. Santoni, A. R. Solomon, and S. S. C. Wong, J. High Energy Phys. 03 (2025) 124.
  10. P. Pani, Phys. Rev. D 92, 124030 (2015); 95, 049902(E) (2017).
  11. N. Uchikata, S. Yoshida, and P. Pani, Phys. Rev. D 94, 064015 (2016).
  12. T. Hinderer, Astrophys. J. 677, 1216 (2008); 697, 964(E) (2009).
  13. T. Hinderer, B. D. Lackey, R. N. Lang, and J. S. Read, Phys. Rev. D 81, 123016 (2010).
  14. T. Damour and A. Nagar, Phys. Rev. D 80, 084035 (2009).
  15. M. Prunier, G. Morrás, J. F. N. n. Siles, S. Clesse, J. García-Bellido, and E. Ruiz Morales, Phys. Dark Universe 46, 101582 (2024).
  16. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Astrophys. J. Lett. 970, L34 (2024).
  17. A. M. Green and B. J. Kavanagh, J. Phys. G 48, 043001 (2021).
  18. N. K. Johnson-McDaniel, A. Mukherjee, R. Kashyap, P. Ajith, W. Del Pozzo, and S. Vitale, Phys. Rev. D 102, 123010 (2020).
  19. D. Shoemaker (L. Collaboration), Advanced LIGO anticipated sensitivity curves, Technical Report No. T0900288-v3, LIGO Document, 2010.
  20. S. Hild et al., Classical Quantum Gravity 28, 094013 (2011).
  21. N. Sennett, T. Hinderer, J. Steinhoff, A. Buonanno, and S. Ossokine, Phys. Rev. D 96, 024002 (2017).
  22. V. Cardoso, E. Franzin, A. Maselli, P. Pani, and G. Raposo, Phys. Rev. D 95, 084014 (2017); 95, 089901(A) (2017).
  23. M. Bošković and E. Barausse, J. Cosmol. Astropart. Phys. 02 (2022) 032.
  24. S. L. Shapiro and S. A. Teukolsky, Compact Objects (Wiley, New York, 1983).
  25. S. L. Liebling and C. Palenzuela, Living Rev. Relativity 26, 1 (2023).
  26. N. Siemonsen and W. E. East, Phys. Rev. D 103, 044022 (2021).
  27. N. M. Santos, C. L. Benone, and C. A. R. Herdeiro, J. Cosmol. Astropart. Phys. 06 (2024) 068.
  28. L. G. Collodel and D. D. Doneva, Phys. Rev. D 106, 084057 (2022).

Outline

Information

Phys. Rev. D 114, 104007– Published 3 November, 2026
  • Received 21 April 2026
  • Accepted 14 September 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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation