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

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Relativistic accretion flow in a generic class of spherically symmetric static spacetimes

Pradeepkumar Yadav*, Sayan Chakrabarti†, and Santabrata Das‡

  • *Contact author: pradeepphy@iitg.ac.in
  • †Contact author: sayan.chakrabarti@iitg.ac.in
  • ‡Contact author: sbdas@iitg.ac.in
PDF

Phys. Rev. D 113, 124035 – Published 11 June, 2026

DOI: https://doi.org/10.1103/p2dn-499w

Abstract

We investigate the properties of low angular momentum, inviscid, advective accretion flows in a generic static and spherically symmetric spacetime that incorporates higher-order corrections up to the fourth order in 1/r. Employing this metric, we self-consistently solve the relativistic hydrodynamical equations and obtain the family of global transonic accretion solutions (O, A, W, and I types) by means of the spacetime parameters (δ,η,β) and the flow parameters (specific energy E and angular momentum λ). Our analysis reveals that the accretion flow possesses either single or multiple critical points depending on these input parameters. We delineate the regions of the δ−λ and λ−ℰ parameter spaces that admits solutions with multiple critical points and demonstrate how these regions evolve with increasing spacetime parameter δ. Furthermore, while connecting the spacetime geometry with observable signatures, we compute the spectral energy distribution (SED) from thermal bremsstrahlung emission and observe that increasing δ enhances the SED relative to the Schwarzschild case. Finally, we find that global transonic solutions harboring inner critical points (I types) yield more luminous power than those with only outer critical points (O and A types).

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (69)

  1. S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs and Neutron Stars. The Physics of Compact Objects (John Wiley & Sons, New York, USA, 1983), 10.1002/9783527617661.
  2. J. Frank, A. King, and D. J. Raine, Accretion Power in Astrophysics: Third Edition (Cambridge University Press, Cambridge, 2002).
  3. Y. Shen and L. C. Ho, Nature (London) 513, 210 (2014).
  4. J. Dexter and E. Agol, Astrophys. J. Lett. 727, L24 (2011).
  5. D. Proga, Astrophys. J. 661, 693 (2007).
  6. B. M. Peterson, An Introduction to Active Galactic Nuclei (Cambridge University Press, Cambridge, 1997).
  7. A. C. Fabian, Annu. Rev. Astron. Astrophys. 50, 455 (2012).
  8. A. A. Esin, J. E. McClintock, and R. Narayan, Astrophys. J. 489, 865 (1997).
  9. S. W. Davis, C. Done, and O. M. Blaes, Astrophys. J. 647, 525 (2006).
  10. I. V. Igumenshchev and M. A. Abramowicz, Mon. Not. R. Astron. Soc. 303, 309 (1999).
  11. J. Li, J. Ostriker, and R. Sunyaev, Astrophys. J. 767, 105 (2013).
  12. F. Yuan and R. Narayan, Annu. Rev. Astron. Astrophys. 52, 529 (2014).
  13. D. F. Torres, Nucl. Phys. B626, 377 (2002).
  14. F. S. Guzmán, Phys. Rev. D 73, 021501 (2006).
  15. T. Harko, Z. Kovács, and F. S. N. Lobo, Phys. Rev. D 79, 064001 (2009).
  16. T. Harko, Z. Kovács, and F. S. N. Lobo, Classical Quantum Gravity 26, 215006 (2009).
  17. Z. Kovács, K. S. Cheng, and T. Harko, Mon. Not. R. Astron. Soc. 400, 1632 (2009).
  18. P. S. Joshi, D. Malafarina, and R. Narayan, Classical Quantum Gravity 31, 015002 (2014).
  19. Z. Kovács and T. Harko, Phys. Rev. D 82, 124047 (2010).
  20. T. Harko, Z. Kovács, and F. S. N. Lobo, Classical Quantum Gravity 27, 105010 (2010).
  21. C. S. J. Pun, Z. Kovács, and T. Harko, Phys. Rev. D 78, 084015 (2008).
  22. M. Heydari-Fard, Classical Quantum Gravity 27, 235004 (2010).
  23. T. Harko, Z. Kovács, and F. S. N. Lobo, Classical Quantum Gravity 28, 165001 (2011).
  24. T. Harko, Z. Kovács, and F. S. N. Lobo, Phys. Rev. D 80, 044021 (2009).
  25. A. Uniyal, S. Chakrabarti, and S. Das, Phys. Dark Universe 44, 101429 (2024).
  26. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, 2018), 10.1017/9781316338612.
  27. B. P. Abbott et al., Phys. Rev. Lett. 116, 131103 (2016).
  28. T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis, Phys. Rep. 513, 1 (2012).
  29. S. Nojiri and S. D. Odintsov, Phys. Rep. 505, 59 (2011).
  30. G. Nordström, Koninklijke Nederlandse Akademie van Wetenschappen Proceedings Series B Physical Sciences vol. 20, p. 1238 (North-Holland Publishing Company, Amsterdam, 1918).
  31. R.-G. Cai, Phys. Rev. D 65, 084014 (2002).
  32. D. Lovelock, J. Math. Phys. (N.Y.) 12, 498 (1971).
  33. N. Dadhich, R. Maartens, P. Papadopoulos, and V. Rezania, Phys. Lett. B 487, 1 (2000).
  34. G. G. Kirilin and I. B. Khriplovich, Sov. J. Exp. Theor. Phys. 95, 981 (2002).
  35. N. E. Bjerrum-Bohr, J. F. Donoghue, and B. R. Holstein, Phys. Rev. D 67, 084033 (2003).
  36. R. Casadio, A. Fabbri, and L. Mazzacurati, Phys. Rev. D 65, 084040 (2002).
  37. S. Devi, A. N. Seenivasan, S. Chakrabarti, and B. R. Majhi, Phys. Dark Universe 39, 101173 (2023).
  38. S. Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon Press, Oxford, 1998).
  39. V. Cardoso and P. Pani, Living Rev. Relativity 22, 4 (2019).
  40. J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973).
  41. M. G. Mafuz, R. Diwan, S. Jana, and S. Kar, Eur. Phys. J. Plus 139, 219 (2024).
  42. I. Chattopadhyay and D. Ryu, Astrophys. J. 694, 492 (2009).
  43. V. V. Kiselev, Classical Quantum Gravity 20, 1187 (2003).
  44. Y. Heydarzade and F. Darabi, Phys. Lett. B 771, 365 (2017).
  45. P. Cañate and S. E. P. Bergliaffa, Phys. Rev. D 102, 104038 (2020).
  46. S. K. Chakrabarti, Astrophys. J. 347, 365 (1989).
  47. S. Das, I. Chattopadhyay, and S. K. Chakrabarti, Astrophys. J. 557, 983 (2001).
  48. I. K. Dihingia, S. Das, D. Maity, and A. Nandi, Mon. Not. R. Astron. Soc. 488, 2412 (2019).
  49. I. K. Dihingia, S. Das, D. Maity, and S. Chakrabarti, Phys. Rev. D 98, 083004 (2018).
  50. H. Riffert and H. Herold, Astrophys. J. 450, 508 (1995).
  51. J. Peitz and S. Appl, Accretion Disks—New Aspects, Lecture Notes in Physics Vol. 487 (Springer, Berlin, Heidelberg, 1997), p. 209, 10.1007/BFb0105834.
  52. I. K. Dihingia, S. Das, and A. Nandi, Mon. Not. R. Astron. Soc. 484, 3209 (2019).
  53. G. Sen, D. Maity, and S. Das, J. Cosmol. Astropart. Phys. 08 (2022) 048.
  54. I. Chattopadhyay and R. Kumar, Mon. Not. R. Astron. Soc. 459, 3792 (2016).
  55. I. K. Dihingia, D. Maity, S. Chakrabarti, and S. Das, Phys. Rev. D 102, 023012 (2020).
  56. E. P. T. Liang and K. A. Thompson, Astrophys. J. 240, 271 (1980).
  57. S. Das, Mon. Not. R. Astron. Soc. 376, 1659 (2007).
  58. R. Kumar, C. B. Singh, I. Chattopadhyay, and S. K. Chakrabarti, Mon. Not. R. Astron. Soc. 436, 2864 (2013).
  59. S. Kato, X.-B. Wu, L.-T. Yang, and Z.-L. Yang, Mon. Not. R. Astron. Soc. 260, 317 (1993).
  60. S. K. Chakrabarti and S. Das, Mon. Not. R. Astron. Soc. 349, 649 (2004).
  61. S. Mitra and S. Das, Astrophys. J. 971, 28 (2024).
  62. J. Quenby, Foundations of High-Energy Astrophysics, edited by M. Vietri (University of Chicago Press, USA, 2010), pp. 445–446, 10.1080/00107510903303667.
  63. T. Okuda, C. B. Singh, S. Das, R. Aktar, A. Nandi, and E. M. d. G. Dal Pino, Publ. Astron. Soc. Jpn. 71, 49 (2019).
  64. I. D. Novikov and K. S. Thorne, Black Holes (Les Astres Occlus) (Gordon and Breach, Science Publishers, Paris, 1973), p. 343.
  65. W. J. Karzas and R. Latter, Astrophys. J. Suppl. Ser. 6, 167 (1961).
  66. I. Chattopadhyay and S. K. Chakrabarti, Mon. Not. R. Astron. Soc. 333, 454 (2002).
  67. G. Sen, D. Maity, and S. Das, J. Cosmol. Astropart. Phys. 10 (2024) 068.
  68. S. Patra, B. R. Majhi, and S. Das, J. Cosmol. Astropart. Phys. 01 (2024) 060.
  69. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications Inc., New York, 1965).

Outline

Information

Phys. Rev. D 113, 124035– Published 11 June, 2026
  • Received 14 December 2025
  • Accepted 8 May 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation