Skip to main content

Advertisement

SpringerLink
Log in

Anisotropic compact stars with Karmarkar condition in energy-momentum squared gravity

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

The main objective of this paper is to examine the viability and stability of anisotropic compact stellar objects adopting the Karmarkar condition in energy-momentum squared gravity. For this purpose, we take a static spherical metric in the inner and Schwarzschild spacetime in the outer region of the stars. The values of unknown parameters are found by the observational values of mass and radius of the considered compact stars. We consider a particular model of this theory to investigate the behavior of energy density, pressure components, anisotropy, equation of state parameters and energy bounds in the inner region of the proposed stellar objects. The equilibrium state of the stellar models is examined via the Tolman–Oppenheimer–Volkoff equation and their stability is analyzed by causality condition, Herrera cracking approach and adiabatic index. We find that Karmarkar solutions in this modified theory are physically viable and stable for anisotropic stellar objects.

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
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data Availability

No new data were generated or analyzed in support of this research.

References

  1. Baade, W., Zwicky, F.: Phys. Rev. 46, 76 (1934)

    Article  ADS  Google Scholar 

  2. Longair, M.S.: High Energy Astrophysics. Cambridge Univeristy Press, Cambridge (1994)

    Book  Google Scholar 

  3. Dev, K., Gleiser, M.: Gen. Relativ. Gravit. 39, 1793 (2002)

    Article  Google Scholar 

  4. Dev, K., Gleiser, M.: Gen. Relativ. Gravit. 35, 1435 (2003)

    Article  ADS  Google Scholar 

  5. Mak, M.K., Harko, T.: Int. J. Mod. Phys. D 13, 149 (2004)

    Article  ADS  Google Scholar 

  6. Kalam, M., et al.: Eur. Phys. J. C 72, 2248 (2012)

    Article  ADS  Google Scholar 

  7. Rahaman, F., et al.: Gen. Relativ. Gravit. 44, 107 (2012)

    Article  ADS  Google Scholar 

  8. Rahaman, F., et al.: Eur. Phys. J. C 72, 2071 (2012)

    Article  ADS  Google Scholar 

  9. Bowers, R.L., Liang, E.P.T.: Astrophys. J. 188, 657 (1974)

    Article  ADS  Google Scholar 

  10. Herrera, L., Santos, N.O.: Phys. Rep. 286, 53 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  11. Harko, T., Mak, M.K.: Ann. Phys. 11, 3 (2002)

    Article  Google Scholar 

  12. Hossein, S.K.M., et al.: Int. J. Mod. Phys. D 21, 1250088 (2012)

    Article  ADS  Google Scholar 

  13. Kalam, M., et al.: Int. J. Theor. Phys. 52, 3319 (2013)

    Article  Google Scholar 

  14. Paul, B.C., Deb, R.: Astrophys. Space Sci. 354, 421 (2014)

    Article  ADS  Google Scholar 

  15. Eisenhart, L.P.: Riemannian Geometry. Princeton University Press, Princeton (1925)

    MATH  Google Scholar 

  16. Maurya, S.K., et al.: Eur. Phys. J. A 52, 191 (2016)

    Article  ADS  Google Scholar 

  17. Maurya, S.K., et al.: Eur. Phys. J. C 76, 266 (2016)

    Article  ADS  Google Scholar 

  18. Singh, K.N., Pant, N.: Eur. Phys. J. C 76, 524 (2016)

    Article  ADS  Google Scholar 

  19. Bhar, P., et al.: Int. J. Mod. Phys. D 26, 1750078 (2017)

    Article  ADS  Google Scholar 

  20. Abbott, B.P., et al.: Phys. Rev. Lett. 116, 061102 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  21. Capozziello, S., De Laurentis, M.: Phys. Rep. 509, 167 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  22. Cognola, G., et al.: Phys. Rev. D 77, 046009 (2008)

    Article  ADS  Google Scholar 

  23. Felice, A.D., Tsujikawa, S.R.: Living Rev. Relativ. 13, 3 (2010)

    Article  ADS  Google Scholar 

  24. Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  25. Harko, T., et al.: Phys. Rev. D 84, 024020 (2011)

    Article  ADS  Google Scholar 

  26. Sharif, M., Gul, M.Z.: Mod. Phys. Lett. A 36, 21502014 (2021)

    Google Scholar 

  27. Haghani, Z., et al.: Phys. Rev. D 88, 044023 (2013)

    Article  ADS  Google Scholar 

  28. Katirci, N., Kavuk, M.: Eur. Phys. J. Plus 129, 163 (2014)

    Article  Google Scholar 

  29. Board, C.V.R., Barrow, J.D.: Phys. Rev. D 96, 123517 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  30. Nari, N., Roshan, M.: Phys. Rev. D 98, 024031 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  31. Bahamonde, S., Marciu, M., Rudra, P.: Phys. Rev. D 100, 083511 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  32. Rudra, P., Pourhassan, B.: Phys. Dark Univ. 33, 100849 (2021)

    Article  Google Scholar 

  33. Ranjit, C., Rudra, P., Kundu, S.: Ann. Phys. 428, 168432 (2021)

    Article  Google Scholar 

  34. Sharif, M., Gul, M.Z.: Phys. Scr. 96, 025002 (2021)

    Article  ADS  Google Scholar 

  35. Sharif, M., Gul, M.Z.: Phys. Scr. 96, 125007 (2021)

    Article  ADS  Google Scholar 

  36. Sharif, M., Gul, M.Z.: Eur. Phys. J. Plus 136, 503 (2021)

    Article  Google Scholar 

  37. Sharif, M., Gul, M.Z.: Chin. J. Phys. 80, 58 (2022)

    Article  Google Scholar 

  38. Sharif, M., Gul, M.Z.: J. Exp. Theor. Phys. (to appear 2022)

  39. Sharif, M., Gul, M.Z.: Int. J. Mod. Phys. A 36, 2150004 (2021)

    Article  ADS  Google Scholar 

  40. Sharif, M., Gul, M.Z.: Chin. J. Phys. 71, 365 (2021)

    Article  Google Scholar 

  41. Sharif, M., Gul, M.Z.: Universe 7, 154 (2021)

    Article  ADS  Google Scholar 

  42. Sharif, M., Gul, M.Z.: Int. J. Geom. Methods Mod. Phys. 19, 2250012 (2022)

    Article  Google Scholar 

  43. Sharif, M., Gul, M.Z.: Mod. Phys. Lett. A 37, 2250005 (2022)

    Article  ADS  Google Scholar 

  44. Astashenok, A.V., Capozziello, S., Odintsov, S.D.: Phys. Rev. D 89, 103509 (2014)

    Article  ADS  Google Scholar 

  45. Sharif, M., Waseem, A.: Can. J. Phys. 94, 1024 (2016)

    Article  ADS  Google Scholar 

  46. Sharif, M., Gul, M.Z.: Eur. Phys. J. Plus 133, 345 (2018)

    Article  Google Scholar 

  47. Sharif, M., Gul, M.Z.: Chin. J. Phys. 57, 329 (2019)

    Article  Google Scholar 

  48. Sharif, M., Gul, M.Z.: Int. J. Mod. Phys. D 28, 1950054 (2019)

    Article  ADS  Google Scholar 

  49. Sharif, M., Ramzan, A.: Phys. Dark Univ. 30, 100737 (2020)

    Article  Google Scholar 

  50. Sharif, M., Ramzan, A.: Astrophys. Space Sci. 365, 1 (2020)

    Article  Google Scholar 

  51. Sharif, M., Naeem, A.: Chin. J. Phys. 66, 765 (2020)

    Article  Google Scholar 

  52. Sharif, M., Naeem, A.: Int. J. Mod. Phys. A 35, 2050121 (2020)

    Article  ADS  Google Scholar 

  53. Rahaman, M., et al.: Eur. Phys. J. C 80, 1 (2020)

    Article  Google Scholar 

  54. Sharif, M., Gul, M.Z.: Adv. Astron. 2021, 6663502 (2021)

    Article  ADS  Google Scholar 

  55. Roshan, M., Shojai, F.: Phys. Rev. D 94, 044002 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  56. Sharif, M., Gul, M.Z.: Phys. Scr. 96, 105001 (2021)

    Article  ADS  Google Scholar 

  57. Sharif, M., Gul, M.Z.: Pramana J. Phys. 96, 153 (2022)

    Article  ADS  Google Scholar 

  58. Akarsu, O., Barrow, J.D., Uzun, N.M.: Phys. Rev. D 102, 124059 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  59. Heintzmann, H., Hillebrandt, W.: Astron. Astrophys. 38, 51 (1975)

    ADS  Google Scholar 

  60. Eiesland, J.: Trans. Am. Math. Soc. 27, 213 (1925)

    Article  MathSciNet  Google Scholar 

  61. Lake, K.: Phys. Rev. D 67, 104015 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  62. Goswami, R., et al.: Phys. Rev. D 90, 084011 (2014)

    Article  ADS  Google Scholar 

  63. Starobinsky, A.A.: Phys. Lett. B 91, 99 (1980)

    Article  ADS  Google Scholar 

  64. Gottlober, S., Muller, V., Satrobinsky, A.A.: Phys. Rev. D 43, 2510 (1991)

    Article  ADS  Google Scholar 

  65. Cembrsnos, J.A.R.: Phys. Rev. Lett. 102, 141301 (2009)

    Article  ADS  Google Scholar 

  66. Cembrsnos, J.A.R.: J. Phys. Conf. Ser. 315, 012004 (2011)

    Article  Google Scholar 

  67. Moraes, P.H.R.S., Correa, R.A.C., Ribeiro, G.: arXiv:1701.01027

  68. Sharif, M., Siddiqa, A.: Int. J. Mod. Phys. D 27, 1850065 (2018)

    Article  ADS  Google Scholar 

  69. Deb, D., et al.: Ann. Phys. 387, 239 (2017)

    Article  ADS  Google Scholar 

  70. Gokhroo, M.K., Mehra, A.L.: Gen. Relativ. Gravit. 26, 75 (1994)

    Article  ADS  Google Scholar 

  71. Singh, K.N., et al.: Eur. Phys. J. A 53, 21 (2017)

    Article  ADS  Google Scholar 

  72. Buchdahl, A.H.: Phys. Rev. D 116, 1027 (1959)

    Article  ADS  Google Scholar 

  73. Ivanov, B.V.: Phys. Rev. D 65, 104011 (2002)

    Article  ADS  Google Scholar 

  74. Tolman, R.C.: Phys. Rev. 55, 364 (1939)

    Article  ADS  Google Scholar 

  75. Oppenheimer, J.R., Volkoff, G.M.: Phys. Rev. 55, 374 (1939)

    Article  ADS  Google Scholar 

  76. Abreu, H., et al.: Class. Quantum Grav. 24, 4631 (2007)

    Article  ADS  Google Scholar 

  77. Herrera, L.: Phys. Lett. A 165, 206 (1992)

    Article  ADS  Google Scholar 

  78. Chandrasekhar, S.: Astrophys. J. 140, 417 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  79. Shamir, M.F., Ahmad, M.: Eur. Phys. J. C 77, 12 (2017)

    Article  Google Scholar 

  80. Sharif, M., Gul, M.Z.: Mod. Phys. Lett. A 36, 2150214 (2021)

    Article  ADS  Google Scholar 

  81. Capozziello, S., De Laurentis, M.: Phys. Rep. 509, 167 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  82. Di Valentino, E., et al.: Class. Quant. Grav. 38, 153001 (2021)

    Article  ADS  Google Scholar 

  83. Liu, X., Harko, T., Liang, S.D.: Eur. Phys. J. C 76, 420 (2016)

    Article  ADS  Google Scholar 

  84. Akarsu, O., et al.: Phys. Rev. D 98, 063522 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  85. Acquaviva, G., Kofron, D., Scholtz, M.: Class. Quant. Grav. 35, 095001 (2018)

    Article  ADS  Google Scholar 

  86. Akarsu, O., et al.: Eur. Phys. J. C 79, 846 (2019)

    Article  ADS  Google Scholar 

  87. Faria, M.C.F.: Astron. Astrophys. 625, 127 (2019)

    Article  Google Scholar 

  88. Barbar, A.H., Awad, A.M., AlFiky, M.T.: Phys. Rev. D 101, 044058 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  89. Kazemi, A., et al.: Eur. Phys. J. C 80, 150 (2020)

    Article  ADS  Google Scholar 

  90. Nazari, E., Sarvi, F., Roshan, M.: Phys. Rev. D 102, 064016 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  91. Nazari, E., Sarvi, F., Roshan, M.: Phys. Rev. D 102, 064016 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  92. Akarsu, O., Katirci, N., Kumar, S.: Phys. Rev. D 97, 024011 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  93. Nazari, E.: Phys. Rev. D 105, 104026 (2022)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, The University of Lahore, 1-KM Defence Road, Lahore, Pakistan

    M. Sharif & M. Zeeshan Gul

Authors
  1. M. Sharif
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Zeeshan Gul
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Sharif.

Additional information

Publisher's Note

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

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

Sharif, M., Gul, M.Z. Anisotropic compact stars with Karmarkar condition in energy-momentum squared gravity. Gen Relativ Gravit 55, 10 (2023). https://doi.org/10.1007/s10714-022-03062-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-022-03062-8

Keywords

Search

Navigation