Skip to main content
SpringerLink
Log in

Relativistic stellar modeling with perfect fluid core and anisotropic envelope fluid

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

We investigate the effect of density perturbations and local anisotropy on the stability of stellar matter structures in general relativity using the concept of cracking. Adopting a core-envelope model of a super-dense star, we examine the properties and stability conditions by introducing anisotropic pressure to the envelope region. Furthermore, we propose self-bound compact stars with an anisotropic envelope as a potential progenitor for starquakes. We show how the difference between sound propagation in radial and tangential directions would be used to identify potentially stable regions within a configuration. Due to an increase in the anisotropic parameter, strain energy accumulates in the envelope region and becomes a potential candidate for building-up quake like situation. This stress-energy stored in the envelope region that would be released during a starquake of a self-bound compact star is computed as a function of the magnitude of anisotropy at the core-envelope boundary. Numerical studies for spherically asymmetric compact stars indicate that the stress energy can be as high as \(10^{50}\) erg if the tangential pressure is slightly more significant than the radial pressure. It is happened to be of the same order as the energy associated with giant \(\gamma \)-ray bursts. Thus, the present study will be useful for the correlation studies between starquakes and GRBs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data availability

No data has been used in this paper and the materials used have been cited in appropriate places.

Code availability

Not applicable.

Notes

  1. Magnetars are the most highly magnetized neutron stars in the cosmos (with magnetic field \(10^{13}\)–\(10^{15}\) G).

  2. Not all branches of sequence \(M=M(\rho _{c})\) are stable. This can be unstable by means of radial oscillations. Degenerate stars with \(\text{d}M/\text{d}\rho _{c}<0\) are found to be unstable and will finally collapse toward Neutron stars, or Black holes.

References

  1. N Itoh Prog. Theor. Exp. Phys. 44 291 (1970)

    ADS  Google Scholar 

  2. J Collins and M Perry Phys. Rev. Lett. 34 1353 (1975)

    ADS  Google Scholar 

  3. M de Avellar, J Horvath and L Paulucci Phys. Rev. D 84 043004 (2011)

    ADS  Google Scholar 

  4. J Horvath and P Moraes Int. J. Mod. Phys. D 30 2150016 (2021)

    ADS  Google Scholar 

  5. J Graham and A Fruchter EAS Publ. Series 61 413 (2013)

    Google Scholar 

  6. B Gendre et al ApJ 766 30 (2013)

    ADS  Google Scholar 

  7. P Kumar and B Zhang Phys. Rep. 561 1 (2015)

    ADS  Google Scholar 

  8. E Nakar Phys. Rep. 442 166 (2007)

    ADS  Google Scholar 

  9. E Berger Annu. Rev. Astron. Astrophys. 52 43 (2014)

    ADS  Google Scholar 

  10. R .-X Xu, D Tao and Y Yang Mon. Not. R. Astron. Soc. 373 L85 (2006)

    ADS  Google Scholar 

  11. C Thompson and R Duncan Mon. Not. R. Astron. Soc. 275 255 (1995)

    ADS  Google Scholar 

  12. C Thompson and R C Duncan ApJ 473 322 (1996)

    ADS  Google Scholar 

  13. L Franco, B Link and R I Epstein ApJ 543 987 (2000)

    ADS  Google Scholar 

  14. G Marranghello, C Vasconcellos and J de Freitas Pacheco Phys. Rev. D 66 064027 (2002)

    ADS  Google Scholar 

  15. R Xu ApJ 596 L59 (2003)

    ADS  Google Scholar 

  16. C Peng and R Xu Mon. Not. R. Astron. Soc. 384 1034 (2008)

    ADS  Google Scholar 

  17. A Zhou, R Xu, X Wu and N Wang Astropart. Phys. 22 73 (2004)

    ADS  Google Scholar 

  18. Z Berezhiani, I Bombaci, A Drago, F Frontera and A Lavagno Nuclear Phys. B Proc. Suppl. 113 268 (2002)

    ADS  Google Scholar 

  19. R Ouyed and F Sannino Astron. Astrophys. 387 725 (2002)

    ADS  Google Scholar 

  20. J Graham et al ApJ 698 1620 (2009)

    ADS  Google Scholar 

  21. A Soderberg et al ApJ 650 261 (2006)

    ADS  Google Scholar 

  22. J Horvath Mod. Phys. Lett. A 20 2799 (2005)

    ADS  Google Scholar 

  23. S Chandrasekhar Phys. Rev. Lett. 12 114 (1964)

    MathSciNet  ADS  Google Scholar 

  24. K Dev and M Gleiser Gen. Relativ. Gravit. 35 1435 (2003)

    ADS  Google Scholar 

  25. L Herrera Phys. Lett. A 165 206 (1992)

    ADS  Google Scholar 

  26. A Di Prisco, E Fuenmayor, L Herrera and V Varela Phys. Lett. A 195 23 (1994)

    MathSciNet  ADS  Google Scholar 

  27. R Chan, L Herrera and N Santos Mon. Not. R. Astron. Soc. 265 533 (1993)

    ADS  Google Scholar 

  28. A Di Prisco, L Herrera and V Varela Gen. Relativ. Gravit. 29 1239 (1997)

    ADS  Google Scholar 

  29. L Herrera and N Santos Phys. Rep. 286 53 (1997)

    MathSciNet  ADS  Google Scholar 

  30. M Mak and T Harko Proc. R. Soc. Lond. Series A Math. Phys. Eng. Sci. 459 393 (2003)

    ADS  Google Scholar 

  31. G Lemaître. Annales de la Société scientifique de Bruxelles, 53, p 51 (1933)

  32. R Bowers and E Liang Astrophys. J. 188 657 (1974)

    ADS  Google Scholar 

  33. W Hillebrandt and K Steinmetz Astron. Astrophys. 53 283 (1976)

    ADS  Google Scholar 

  34. G Sagar, B Pandey and N Pant Astrophys. Space Sci. 367 72 (2022)

    ADS  Google Scholar 

  35. N Pant, S Gedela, R Pant, J Upreti and R K Bisht Eur. Phys. J. Plus 135 1 (2020)

    Google Scholar 

  36. V Thomas, B Ratanpal and P Vinodkumar Int. J. Mod. Phys. D 14 85 (2005)

    ADS  Google Scholar 

  37. R Tikekar and V Thomas Pramana 64 5 (2005)

    ADS  Google Scholar 

  38. P Mafa Takisa and S Maharaj Astrophys. Space Sci. 361 1 (2016)

    Google Scholar 

  39. S Gedela, N Pant, J Upreti and R Pant Eur. Phys. J. C 79 1 (2019)

    Google Scholar 

  40. S Mardan, I Noureen and A Khalid Eur. Phys. J. C 81 1 (2021)

    Google Scholar 

  41. N Pant, S Gedela and R K Bisht Chin. J. Phys. 72 530 (2021)

    Google Scholar 

  42. S Gedela, R K Bisht and N Pant Mod. Phys. Lett. A 35 2050097 (2020)

    ADS  Google Scholar 

  43. H Abreu, H Hernandez and L Nunez Class. Quantum Gravity 24 4631 (2007)

    ADS  Google Scholar 

  44. G González, A Navarro and L Núnez. J. Phys. Conf. Ser. 600 012014. IOP Publishing (2015)

  45. B Ratanpal IOP SciNotes 1 025207 (2020)

    ADS  Google Scholar 

  46. E Annala, T Gorda, A Kurkela, J Nättilä and A Vuorinen Nat. Phys. 16 907 (2020)

    Google Scholar 

  47. A Khunt, V Thomas and P Vinodkumar Int. J. Mod. Phys. D 30 2150029 (2021)

    ADS  Google Scholar 

  48. X Shu, Y Huang and H Zong Mod. Phys. Lett. A 32 1750027 (2017)

    ADS  Google Scholar 

  49. B Link, L Franco and R Epstein Astrophys. J. 508 838 (1998)

    ADS  Google Scholar 

  50. S Weinberg. Gravitation and cosmology: principles and applications of the general theory of relativity (John Wiley) (1972)

  51. A Sulaksono Int. J. Mod. Phys. E 24 1550007 (2015)

    ADS  Google Scholar 

  52. A Setiawan and A Sulaksono Eur. Phys. J. C 79 1 (2019)

    Google Scholar 

  53. J Lattimer Annu. Rev. Nucl. Part. Sci. 62 485 (2012)

    ADS  Google Scholar 

  54. B Abbott et al Phys. Rev. lett. 121 161101 (2018)

    ADS  Google Scholar 

  55. M Miller et al Astrophys. J. Lett. 887 L24 (2019)

    ADS  Google Scholar 

  56. Y Zeldovich and I Novikov. (Chicago: University of Chicago Press) (1971)

  57. B Harrison, K Throne, M Wakano and J Wheeler. Gravitational Theory and Gravitational Collapse (University of Chicago Press) (1965)

  58. S Saklany, N Pant and B Pandey Phys. Dark Universe. 39 101166 (2023)

    Google Scholar 

  59. T Riley et al Astrophys. J. Lett. 887 L21 (2019)

    ADS  Google Scholar 

  60. J Lattimer and M Prakash Astrophys. J. 550 426 (2001)

    ADS  Google Scholar 

  61. Zel’dovich. Sov. Phys. JETP 14 (1962)

  62. P Bedaque and A W Steiner Phys. Rev. lett. 114 031103 (2015)

    ADS  Google Scholar 

  63. B Reed and C Horowitz Phys. Rev. C 101 045803 (2020)

    ADS  Google Scholar 

  64. C C Moustakidis, T Gaitanos, C Margaritis and G Lalazissis Phys. Rev. C 95 045801 (2017)

    ADS  Google Scholar 

  65. E Van Oeveren and J Friedman Phys. Rev. D 95 083014 (2017)

    ADS  Google Scholar 

  66. Y Ma and M Rho Phys. Rev. D 100 114003 (2019)

    ADS  Google Scholar 

  67. H Bondi Proc. R. Soc. Lond. Series A Math. Phys. Sci. 281 39 (1964)

    ADS  Google Scholar 

  68. P Haensel, A Potekhin and D Yakovlev. Neutron Stars 1 (Springer) (2007)

  69. D Ravenhall and C Pethick Astrophys. J. 424 846 (1994)

    ADS  Google Scholar 

  70. K Thorne Astrophys. J. 212 825 (1977)

    ADS  Google Scholar 

  71. O Blaes, R Blandford, P Goldreich and P Madau ApJ 343 839 (1989)

    ADS  Google Scholar 

  72. P Mock and P Joss ApJ 500 374 (1998)

    ADS  Google Scholar 

  73. A Watts et al Rev. Mod. Phys. 88 021001 (2016)

    ADS  Google Scholar 

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Physics, Sardar Patel University, Vallabh Vidynagar, Gujarat, 388 120, India

    A. C. Khunt & P. C. Vinodkumar

  2. Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, 390 002, India

    V. O. Thomas

  3. Department of Physical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa, Gujarat, 388 421, India

    P. C. Vinodkumar

Authors
  1. A. C. Khunt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. O. Thomas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. C. Vinodkumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

(i) Khunt: Conceptualization, methodology, analytical and numerical calculation, manuscript preparation; (ii) Thomas: investigation, writing-review,; (iii) Vinodkumar: writing-review, calculation-analysis.

Corresponding author

Correspondence to A. C. Khunt.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A: Anisotropy profile

Appendix A: Anisotropy profile

In this appendix, we show anisotropy plot for values of \(\lambda =\) 0.1, 0.3, 0.5, and 0.9 from the TRV model presented in Subsect. 2.1.2 (Fig. 11).

Fig. 11
figure 11

Variation of an anistropy S in km\(^{-2}\) with respect to a envelope radius of the star. For a density variation of \(\;\; \lambda =0.1, 0.3, 0.5 \;\; \text {and}, 0.9\) (color figure online)

Full size image

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khunt, A.C., Thomas, V.O. & Vinodkumar, P.C. Relativistic stellar modeling with perfect fluid core and anisotropic envelope fluid. Indian J Phys 97, 3379–3393 (2023). https://doi.org/10.1007/s12648-023-02692-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-023-02692-1

Keywords

Search

Navigation