Research ArticleNo Access

Relativistic configurations of Tolman Stellar structures in Gauss–Bonnet gravity

Adnan Malik

https://orcid.org/0000-0002-6034-0117

School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang, P. R. China

Department of Mathematics, University of Management and Technology, Sialkot Campus, Lahore, Pakistan

E-mail Address: adnan.malik@zjnu.edu.cn

E-mail Address: adnan.malik@skt.umt.edu.pk

E-mail Address: adnanmalik_chheena@yahoo.com

Search for more papers by this author

Tayyaba Naz

https://orcid.org/0000-0002-2452-6838

National University of Computer and Emerging Sciences, Lahore Campus, Pakistan

E-mail Address: tayyaba.naz@nu.edu.pk

Search for more papers by this author

Yonghui Xia

https://orcid.org/0000-0001-8918-3509

School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang, P. R. China

E-mail Address: xiadoc@163.com

Corresponding author.

Search for more papers by this author

, and

Humaira Asghar

https://orcid.org/0009-0004-2667-5820

Department of Mathematics, University of Management and Technology, Sialkot Campus, Lahore, Pakistan

E-mail Address: humairaasghar115@gmail.com

Search for more papers by this author

https://doi.org/10.1142/S0219887824500919Cited by:6 (Source: Crossref)

Abstract

The purpose of this study is to discuss the charged stellar structure in the background of the $f (𝒢)$ theory of gravity. The Einstein–Maxwell equations defined in the appearance of charge by utilizing the Tolman–Kuchowicz spacetime are described by spherically symmetric spacetime. To analyze the charged stellar structure, we use the matching conditions of spherically symmetric spacetime with the Reissner–Nordström exterior metric and develop some expressions for examining the energy density, radial pressure and tangential pressure, respectively. We address the energy conditions to verify our model’s viability for the SAX J1808.4-3658 star. Some other physical features, such as energy density, pressure components, anisotropic parameters, equation of state parameters, stability analysis, adiabatic index, Tolman–Oppenheimer–Volkoff equation, mass-radius relationship, compactness and redshift, have been investigated. We observe that our results are physically viable, free from geometrical and physical singularities, which provide circumstantial evidence for the existence of viable and stable compact star.

Keywords:

References

1. J. B. Jimenez et al., Cosmic vector for dark energy, Phys. Rev. D 78(6) (2008) 063005. Crossref, Web of Science, Google Scholar
2. P. M. Garnavich et al., Supernova limits on the cosmic equation of state, Astrophys. J. 509(1) (1998) 74. Crossref, Web of Science, Google Scholar
3. G. J. Mathews et al., Big bang nucleosynthesis with a new neutron lifetime. Phys. Rev. D 71(2) (2005) 021302. Crossref, Web of Science, Google Scholar
4. M. Tegmartk et al., Cosmological parameters from SDSS and WMAP, Phys. Rev. D 69(10) (2004) 103501. Crossref, Web of Science, Google Scholar
5. D. Wang et al., Observational constraints on a logarithmic scalar field dark energy model and black hole mass evolution in the universe, Eur. Phys. J. C 83 (2023) 670. Crossref, Web of Science, Google Scholar
6. A. Malik et al., A comprehensive discussion for the identification of cracking points in $f (R)$ theories of gravity, Eur. Phys. J. C 83 (2023) 765. Crossref, Web of Science, Google Scholar
7. S. A. Mardan et al., Spherically symmetric generating solutions in $f (R)$ theory, Eur. Phys. J. Plus 138(9) (2023) 782. Crossref, Web of Science, Google Scholar
8. M. F. Shamir and A. Malik, Bardeen compact stars in modified $f (R)$ gravity, Chin. J. Phys. 69 (2021) 312–321. Crossref, Web of Science, Google Scholar
9. A. Malik et al., Investigation of traversable wormhole solutions in modified $f (R)$ gravity with scalar potential, Eur. Phys. J. C 83 (2023) 522. Crossref, Web of Science, Google Scholar
10. T. Naz et al., Evolving embedded traversable wormholes in $f (R, G)$ gravity: A comparative study, Phys. Dark Univ. 42 (2023) 101301. Crossref, Web of Science, Google Scholar
11. S. Nojiri and S. D. Odintsov, Modified Gauss–Bonnet theory as gravitational alternative for dark energy, Phys. Lett. B 631(1–2) (2005) 1–6. Crossref, Web of Science, Google Scholar
12. Z. Yousaf et al., Stability of anisotropy pressure in self-gravitational systems in $f (G)$ gravity, Axioms 12(3) (2023) 257. Crossref, Web of Science, Google Scholar
13. Z. Yousaf et al., Bouncing cosmology with 4D-EGB gravity, Int. J. Theor. Phys. 62 (2023) 155. Crossref, Web of Science, Google Scholar
14. A. Malik et al., Bardeen compact stars in modified $f (G)$ gravity, Can. J. Phys. 100(10) (2022) 452–462. Crossref, Google Scholar
15. Z. Yousaf et al., Electromagnetic effects on anisotropic expansion-free fluid content, Commun. Theor. Phys. 75 (2023) 105202. Crossref, Web of Science, Google Scholar
16. M. F. Shamir et al., Relativistic Krori–Barua compact stars in $f (R, T)$ gravity, Fortsch. Phys. 70(12) (2022) 2200134. Crossref, Web of Science, Google Scholar
17. Z. Asghar et al., Study of embedded class-I fluid spheres in $f (R, T)$ gravity with Karmarkar condition, Chin. J. Phys. 83 (2023) 427–437. Crossref, Web of Science, Google Scholar
18. A. Malik et al., A comprehensive discussion for the identification of cracking points in $f (R, T)$ theory of gravity, Eur. Phys. J. C 83 (2023) 845. Crossref, Web of Science, Google Scholar
19. A. Malik et al., Analysis of charged compact stars in $f (R, T)$ gravity using Bardeen geometry, Int. J. Geom. Methods Mod. Phys. 20(4) (2023) 2350061. Link, Google Scholar
20. T. Naz et al., Relativistic configurations of Tolman Stellar spheres in $f (G, T)$ gravity, Int. J. Geom. Methods Mod. Phys. 20(13) (2023) 2350222. Link, Web of Science, Google Scholar
21. A. Malik, A study of Levi-Civita’s cylindrical solutions in $f (R, ϕ)$ gravity, Eur. Phys. J. Plus 136 (2021) 1146. Crossref, Web of Science, Google Scholar
22. A. Malik, Analysis of charged compact stars in modified $f (R, ϕ)$ theory of gravity, New Astron. 93 (2022) 101765. Crossref, Web of Science, Google Scholar
23. A. Malik et al., Some dark energy cosmological models in $f (R, ϕ)$ gravity, New Astron. 89 (2021) 101631. Crossref, Web of Science, Google Scholar
24. M. F. Shamir and A. Malik, Investigating $f (R, ϕ)$ cosmology with equation of state, Can. J. Phys. 97(7) (2019) 752–760. Crossref, Web of Science, Google Scholar
25. A. Malik et al., Energy bounds in $f (R, ϕ)$ gravity with anisotropic backgrounds, New Astron. 79 (2020) 101392. Crossref, Web of Science, Google Scholar
26. M. F. Shamir et al., Non-commutative wormhole solutions in modified $f (R, ϕ, X)$ gravity, Chin. J. Phys. 73 (2021) 634–648. Crossref, Web of Science, Google Scholar
27. M. F. Shamir et al., Wormhole solutions in modified $f (R, ϕ, X)$ gravity, Int. J. Mod. Phys. A 36 (2021) 2150021. Link, Web of Science, Google Scholar
28. M. F. Shamir et al., Dark $f (R, ϕ, X)$ universe with Noether symmetry, Theor. Math. Phys. 205(3) (2020) 1692–1705. Crossref, Web of Science, Google Scholar
29. A. Malik et al., Noether symmetries of LRS Bianchi type-I space-time in $f (R, ϕ, X)$ gravity, Int. J. Geom. Methods Mod. Phys. 17(11) (2020) 2050163. Link, Web of Science, Google Scholar
30. A. Malik and A. Nafees, Existence of static wormhole solutions in $f (R, ϕ, X)$ gravity, New Astron. 89 (2021) 101632. Crossref, Web of Science, Google Scholar
31. A. Malik et al., A study of Levi-Civita’s cylindrical solutions in $f (R, ϕ, X)$ gravity, Eur. Phys. J. C 82 (2022) 166. Crossref, Web of Science, Google Scholar
32. A. Malik et al., Krori–Barua Bardeen compact stars in $f (R, T)$ gravity, New Astron. 104 (2023) 102071. Crossref, Web of Science, Google Scholar
33. S. K. Maurya et al., Gravitationally decoupled strange star model beyond the standard maximum mass limit in Einstein-Gauss–Bonnet gravity, Astrophys. J. 925(2) (2022) 208. Crossref, Web of Science, Google Scholar
34. S. K. Maurya et al., Observational constraints on maximum mass limit and physical properties of anisotropic strange star models by gravitational decoupling in Einstein–Gauss–Bonnet gravity, Mon. Not. R. Astron. Soc. 519(3) (2023) 4303–4324. Crossref, Web of Science, Google Scholar
35. P. Bhar et al., Physical characteristics and maximum allowable mass of hybrid star in the context of $f (Q)$ gravity, Eur. Phys. J. C 83 (2023) 646. Crossref, Web of Science, Google Scholar
36. Z. Asghar et al., Comprehensive analysis of relativistic embedded class-I exponential compact spheres in $f (R, ϕ)$ gravity via Karmarkar condition, Commun. Theor. Phys. 75 (2023) 105401. Crossref, Web of Science, Google Scholar
37. A. Malik et al., Singularity-free anisotropic strange quintessence stars in $f (R, ϕ)$ theory of gravity, Eur. Phys. J. Plus 138 (2023) 418. Crossref, Web of Science, Google Scholar
38. M. F. Shamir and A. Rashid, Bardeen compact stars in modified $f (R)$ gravity with conformal motion, Int. J. Geom. Methods Mod. Phys. 20(2) (2023) 2350026. Link, Google Scholar
39. J. Santos et al., Energy conditions and cosmic acceleration, Phys. Rev. D 75(8) (2007) 083523. Crossref, Web of Science, Google Scholar
40. M. K. Mak and T. Harko, Can the galactic rotation curves be explained in brane world models? Phys. Rev. D 70(2) (2004) 024010. Crossref, Web of Science, Google Scholar
41. M. Chaisi and S. D. Maharaj, Compact anisotropic spheres with prescribed energy density, Gen. Relativ. Gravit. 37 (2005) 1177–1189. Crossref, Web of Science, Google Scholar
42. F. Rahaman et al., Strange stars in Krori–Barua space-time, Eur. Phys. J. C 72 (2012) 1–9. Crossref, Web of Science, Google Scholar
43. K. N. Singh et al., Anisotropic compact stars in Karmarkar spacetime, Chin. Phys. C 41(1) (2017) 015103. Crossref, Web of Science, Google Scholar
44. P. Bhar, Singularity-free anisotropic strange quintessence star, Astrophys. Space Sci. 356(2) (2015) 309–318. Crossref, Web of Science, Google Scholar
45. P. Bhar, Vaidya–Tikekar type superdense star admitting conformal motion in presence of quintessence field. Eur. Phys. J. C 75 (2015) 1–9. Crossref, Web of Science, Google Scholar
46. K. N. Singh and N. Pant, Charged anisotropic superdense stars with constant stability factor, Astrophys. Space Sci. 358 (2015) 1–13. Crossref, Web of Science, Google Scholar
47. M. F. Shamir and A. Malik, Behavior of anisotropic compact stars in $f (R, ϕ)$ gravity, Commun. Theor. Phys. 71(5) (2019) 599. Crossref, Web of Science, Google Scholar
48. A. Malik et al., A study of anisotropic compact stars in $f (R, ϕ, X)$ theory of gravity, Int. J. Geom. Methods Mod. Phys. 19(2) (2022) 2250028. Link, Web of Science, Google Scholar
49. A. Rashid et al., A comprehensive study of Bardeen stars with conformal motion in $f (G)$ gravity, Eur. Phys. J. C 83 (2023) 997. Crossref, Web of Science, Google Scholar
50. S. V. Lohakare et al., Influence of three parameters on maximum mass and stability of strange star under linear $f (Q)$ -action, Mon. Not. R. Astron. Soc. 526(3) (2023) 3796–3814. Crossref, Web of Science, Google Scholar
51. S. K. Maurya et al., Anisotropic strange star model beyond standard maximum mass limit by gravitational decoupling in $f (Q)$ gravity, Fortsch. Phys. 70(11) (2022) 2200061. Crossref, Web of Science, Google Scholar
52. S. K. Maurya et al., Anisotropic compact stars in complexity formalism and isotropic stars made of anisotropic fluid under minimal geometric deformation (MGD) context in $f (T)$ gravity-theory, Eur. Phys. J. C 83(4) (2023) 348. Crossref, Web of Science, Google Scholar
53. G. G. L. Nashed, Charged dilaton, energy, momentum and angular-momentum in teleparallel theory equivalent to general relativity, Eur. Phys. J. C 54 (2008) 291–302. Crossref, Web of Science, Google Scholar
54. G. G. L. Nashed and T. Shirafuji, Reissner–Nordström space-time in the tetrad theory of gravitation, Int. J. Mod. Phys. D 16(1) (2007) 65–79. Link, Web of Science, Google Scholar
55. G. G. L. Nashed, Reissner–Nordström solutions and energy in teleparallel theory, Mod. Phys. Lett. A 21(29) (2006) 2241–2250. Link, Web of Science, Google Scholar
56. G. G. L. Nashed and S. Capozziello, Stable and self-consistent compact star models in teleparallel gravity, Eur. Phys. J. C 80 (2020) 1–18. Crossref, Web of Science, Google Scholar
57. Z. Roupas and G. G. L. Nashed, Anisotropic neutron stars modelling: Constraints in Krori–Barua spacetime, Eur. Phys. J. C 80 (2020) 1–11. Crossref, Web of Science, Google Scholar
58. W. El Hanafy and G. G. L. Nashed, The hidden flat like universe: Starobinsky-like inflation induced by f (T) gravity, Eur. Phys. J. C 75 (2015) 1–14. Crossref, Google Scholar
59. G. G. L. Nashed, Kerr–Newman solution and energy in teleparallel equivalent of einstein theory, Mod. Phys. Lett. A 22(14) (2007) 1047–1056. Link, Web of Science, Google Scholar
60. G. G. L. Nashed et al., Charged rotating black holes coupled with nonlinear electrodynamics Maxwell field in the mimetic gravity, J. Cosmol. Astropart. Phys. 2019(1) (2019) 058. Crossref, Google Scholar
61. G. G. L. Nashed and S. Nojiri, Nontrivial black hole solutions in $f (R)$ gravitational theory, Phys. Rev. D 102(12) (2020) 124022. Crossref, Web of Science, Google Scholar
62. G. G. L. Nashed and E. N. Saridakis, New rotating black holes in nonlinear Maxwell $f (R)$ gravity, Phys. Rev. D 102(12) (2020) 124072. Crossref, Web of Science, Google Scholar
63. S. Capozziello and G. G. L. Nashed, Rotating and non-rotating AdS black holes in $f (T)$ gravity non-linear electrodynamics, Eur. Phys. J. C 79(11) (2019) 911. Crossref, Web of Science, Google Scholar
64. G. G. L. Nashed, Higher dimensional charged black hole solutions in $f (R)$ gravitational theories, Adv. High Energy Phys. 2018 (2018) 1–16. Crossref, Google Scholar
65. G. G. L. Nashed, Kerr-NUT black hole thermodynamics in $f (T)$ gravity theories, Eur. Phys. J. Plus 130(7) (2015) 124. Crossref, Web of Science, Google Scholar
66. S. K. Maurya and F. Tello-Ortiz, Charged anisotropic compact star in $f (R, T)$ gravity: A minimal geometric deformation gravitational decoupling approach, Phys. Dark Univ. 27 (2020) 100442. Crossref, Web of Science, Google Scholar
67. M. Ilyas, Charged compact stars in $f (G)$ gravity, Eur. Phys. J. C 78(9) (2018) 757. Crossref, Web of Science, Google Scholar
68. P. Bhar et al., Possibility of higher-dimensional anisotropic compact star, Eur. Phys. J. C 75(5) (2015) 190. Crossref, Web of Science, Google Scholar
69. M. Zubair and G. Abbas, Some interior models of compact stars in $f (R)$ gravity, Astrophys. Space Sci. 361(10) (2016) 342. Crossref, Web of Science, Google Scholar
70. M. Farasat Shamir and I. Fayyaz, Charged stellar structure in Tolman–Kuchowicz spacetime, Int. J. Geom. Methods Mod. Phys. 17(9) (2020) 2050140. Link, Web of Science, Google Scholar
71. M. Sharif and A. Waseem, Charged compact objects in $f (R, T)$ gravity, Int. J. Mod. Phys. D 28(2) (2019) 1950033. Link, Web of Science, Google Scholar
72. P. Rej et al., Charged compact star in $f (R, T)$ gravity in Tolman–Kuchowicz spacetime, Eur. Phys. J. C 81(4) (2021) 316. Crossref, Web of Science, Google Scholar
73. M. Javed et al., Anisotropic spheres in $f (R, G)$ gravity with Tolman–Kuchowicz spacetime, New Astron. 84 (2021) 101518. Crossref, Web of Science, Google Scholar
74. M. F. Shamir and I. Fayyaz, Charged stellar structure in Tolman–Kuchowicz spacetime, Int. J. Geom. Methods Mod. Phys. 17(9) (2020) 2050140. Link, Web of Science, Google Scholar
75. M. Zubair et al., Anisotropic compact star models in $f (T)$ gravity with Tolman–Kuchowicz spacetime, Int. J. Geom. Methods Mod. Phys. 18(4) (2021) 2150060. Link, Web of Science, Google Scholar
76. G. G. L. Nashed and S. Capozziello, Anisotropic compact stars in $f (R)$ gravity, Eur. Phys. J. C 81(5) (2021) 481. Crossref, Web of Science, Google Scholar
77. A. V. Astashenok et al., Maximum baryon masses for static neutron stars in $f (R)$ gravity, Europhys. Lett. 136(5) (2022) 59001. Crossref, Google Scholar
78. A. V. Astashenok et al., Causal limit of neutron star maximum mass in $f (R)$ gravity in view of GW190814, Phys. Lett. B 816 (2021) 136222. Crossref, Web of Science, Google Scholar
79. G. G. L. Nashed, Teleparallel equivalent theory of (1+ 1)-dimensional gravity, Chin. Phys. B 19 (2010) 110401. Crossref, Web of Science, Google Scholar
80. G. G. L. Nashed, Spherically symmetric charged black holes in $f (R)$ gravitational theories. Eur. Phys. J. Plus 133 (2018) 18. Crossref, Web of Science, Google Scholar
81. G. G. L. Nashed, Rotating charged black hole spacetimes in quadratic gravitational theories, Adv. High Energy Phys. 2018 (2018) 7323574. Crossref, Web of Science, Google Scholar
82. G. G. L. Nashed et al., Thermodynamical correspondence of $f (R)$ gravity in the Jordan and Einstein frames, Int. J. Mod. Phys. D 29 (2020) 2050090. Link, Web of Science, Google Scholar
83. G. G. L. Nashed, Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity. Eur. Phys. J. C 49 (2007) 851. Crossref, Web of Science, Google Scholar
84. A. V. Astashenok et al., Nonperturbative models of quark stars in $f (R)$ gravity, Phys. Lett. B 742 (2015) 160. Crossref, Web of Science, Google Scholar
85. S. Capozziello et al., Constraining extended gravity models by S2 star orbits around the Galactic Centre, Phys. Rev. D 90 (2014) 044052. Crossref, Web of Science, Google Scholar
86. S. Capozziello et al., Mass-radius relation for neutron stars in $f (R)$ gravity, Phys. Rev. D 93 (2016) 023501. Crossref, Web of Science, Google Scholar
87. S. Capozziello et al., Hydrostatic equilibrium and stellar structure in $f (R)$ gravity, Phys. Rev. D 83 (2011) 064004. Crossref, Web of Science, Google Scholar
88. S. Capozziello, Further stable neutron star models from $f (R)$ gravity, J. Cosmol. Astropart. Phys. 2013 (2013) 040. Crossref, Web of Science, Google Scholar
89. A. Malik, Comprehensive study of cylindrical Levi-Civita and cosmic string solutions in Rastall theory of gravity, Chin. J. Phys. 84 (2023) 357–370. Crossref, Web of Science, Google Scholar
90. A. Malik et al., Embedding procedure and wormhole solutions in Rastall gravity utilizing the class I approach, Int. J. Geom. Methods Mod. Phys. 20 (2023) 2350145. Link, Web of Science, Google Scholar
91. A. Malik et al., Analysis of class I complexity induced spherical polytropic models for compact objects, Front. Astron. Space Sci. 10 (2023) 1182772. Crossref, Web of Science, Google Scholar
92. A. Malik et al., A study of charged stellar structures in modified $f (R, ϕ, X)$ theory of gravity, Int. J. Geom. Methods Mod. Phys. 19(11) (2022) 2250180. Link, Web of Science, Google Scholar
93. A. Malik et al., Traversable wormhole solutions in $f (R)$ theories of gravity Via Karmarkar condition, Chin. Phys. C 46(9) (2022) 095104. Crossref, Web of Science, Google Scholar
94. A. Malik et al., Anisotropic spheres via embedding approach in $f (R)$ gravity, Int. J. Geom. Methods Mod. Phys. 19 (2022) 2250073. Link, Web of Science, Google Scholar
95. K. D. Krori and J. Barua, A singularity-free solution for a charged fluid sphere in general relativity, J. Phys. A: Math. General 8(4) (1975) 508. Crossref, Google Scholar
96. A. Chodos et al., New extended model of hadrons, Phys. Rev. D 9(12) (1974) 3471. Crossref, Web of Science, Google Scholar
97. M. K. Jasim et al., Anisotropic strange stars in Tolman–Kuchowicz spacetime, Eur. Phys. J. C 78(7) (2018) 603. Crossref, Web of Science, Google Scholar
98. K. Bamba et al., Finite-time future singularities in modified Gauss–Bonnet and $f (R, G)$ gravity and singularity avoidance, Eur. Phys. J. C 67 (2010) 295–310. Crossref, Web of Science, Google Scholar
99. D. Deb et al., Study on charged strange stars in $f (R, 𝒯)$ gravity, preprint (2018), arXiv:1812.11736. Google Scholar
100. A. Cooney et al., Neutron stars in $f (R)$ gravity with perturbative constraints, Phys. Rev. D 82(6) (2010) 064033. Crossref, Web of Science, Google Scholar
101. L. Herrera, Cracking of self-gravitating compact objects, Phys. Lett. A 165(3) (1992) 206–210. Crossref, Web of Science, Google Scholar
102. R. C. Tolman, Static solutions of Einstein’s field equations for spheres of fluid, Phys. Rev. 55(4) (1939) 364. Crossref, Google Scholar
103. J. R. Oppenheimer and G. M. Volkof, On massive neutron cores, Phys. Rev. 55(4) (1939) 374. Crossref, Google Scholar
104. W. Hillebrandt and K. O. Steinmetz, Anisotropic neutron star models-stability against radial and nonradial pulsations, Astron. Astrophys. 53 (1976) 283. Web of Science, Google Scholar