Geodesic
Dynamical behavior of stellar structures in $f(\mathcal{G})$ gravity
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 2, pp. 324-345 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the context of modified $f(\mathcal G)$ gravity, we study the appearance of anisotropic compact stellar objects. The space–time geometry is characterized by the metric potentials, and to solve the field equations, we consider their specific form known as the Tolman–Kuchowicz space–time. The obtained solutions are free of singularities and satisfy all requirements for stellar objects. We consider the observational data for models of the stars Cen X-3, EXO 1785-248, and LMC X-4, and taking these data into account, we obtain the values of the physical parameters from the matching conditions for the interior Tolman–Kuchowicz space–time and the exterior Schwarzschild metric. In addition, we discuss some physical attributes of anisotropic compact stellar structures to verify the physical validity and stability of the proposed model. We perform a three-dimensional graphical analysis that allows obtaining a representation of the physical behavior of these compact objects. We note that all three compact objects correspond to physically accepted models.
Keywords: stellar structure, $f(\mathcal G)$ gravity, metric potential. 
@article{TMF_2020_205_2_a7,
     author = {T. Naz and M. F. Shamir},
     title = {Dynamical behavior of stellar structures in $f(\mathcal{G})$ gravity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {324--345},
     year = {2020},
     volume = {205},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_2_a7/}
}
TY  - JOUR
AU  - T. Naz
AU  - M. F. Shamir
TI  - Dynamical behavior of stellar structures in $f(\mathcal{G})$ gravity
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2020
SP  - 324
EP  - 345
VL  - 205
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2020_205_2_a7/
LA  - ru
ID  - TMF_2020_205_2_a7
ER  - 
%0 Journal Article
%A T. Naz
%A M. F. Shamir
%T Dynamical behavior of stellar structures in $f(\mathcal{G})$ gravity
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2020
%P 324-345
%V 205
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2020_205_2_a7/
%G ru
%F TMF_2020_205_2_a7
T. Naz; M. F. Shamir. Dynamical behavior of stellar structures in $f(\mathcal{G})$ gravity. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 2, pp. 324-345. http://geodesic.mathdoc.fr/item/TMF_2020_205_2_a7/

[1] A. G. Riess, A. V. Filippenko, P. Challis et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant”, Astron. J., 116:3 (1998), 1009–1038, arXiv: astro-ph/9805201 | DOI

[2] D. N. Spergel, L. Verde, H. V. Peiris et al., “First-year Wilkinson microwave anisotropy probe (WMAP) observations: determination of cosmological parameters”, Astrophys. J. Suppl. Ser., 148:1 (2003), 175–194, arXiv: astro-ph/0302209 | DOI

[3] D. N. Spergel, R. Bean, O Doré et al., “Three-year Wilkinson microwave anisotropy probe (WMAP) observations: implications for cosmology”, Astrophys. J. Suppl., 170:2 (2007), 377–408, arXiv: astro-ph/0603449 | DOI

[4] S. Nojiri, S. D. Odintsov, “Introduction to modified gravity and gravitational alternative for dark energy”, Internat. J. Geom. Meth. Modern Phys., 4:1 (2007), 115–145 | DOI

[5] S. Nojiri, S. D. Odintsov, “Unified cosmic history in modified gravity: from $F(R)$ theory to Lorentz non-invariant models”, Phys. Rep., 505:2–4 (2011), 59–144, arXiv: 1011.0544 | DOI | MR

[6] S. Nojiri, S. D. Odintsov, V. K. Oikonomou, “Modified gravity theories on a nutshell: inflation, bounce and late-time evolution”, Phys. Rep., 692 (2017), 1–104, arXiv: 1705.11098 | DOI | MR

[7] H. A. Buchdahl, “Non-linear Lagrangians and cosmological theory”, Mon. Not. R. Astron. Soc., 150:1 (1970), 1–8 | DOI

[8] S. Nojiri, S. D. Odintsov, “Modified Gauss–Bonnet theory as gravitational alternative for dark energy”, Phys. Lett. B, 631:1–2 (2005), 1–6, arXiv: hep-th/0508049 | DOI | MR

[9] G. Congnola, E. Elizalde, S. Nojiri, S. D. Odintsov, S. Zerbini, “Dark energy in modified Gauss–Bonnet gravity: late-time acceleration and the hierarchy problem”, Phys. Rev. D, 73:8 (2006), 084007, 16 pp., arXiv: hep-th/0601008 | DOI

[10] G. Congnola, E. Elizalde, S. Nojiri, S. D. Odintsov, S. Zerbini, “String-inspired Gauss–Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy”, Phys. Rev. D, 75:8 (2007), 086002, 17 pp. | DOI | MR

[11] T. Chiba, “Generalized gravity and a ghost”, J. Cosmol. Astropart. Phys., 2005:3 (2005), 008, 7 pp. | DOI | MR

[12] J. Santos, J. S. Alcaniz, N. Pires, M. J. Rebouas, “Energy conditions and cosmic acceleration”, Phys. Rev. D, 75:8 (2007), 083523, 6 pp., arXiv: astro-ph/0702728 | DOI | MR

[13] M. K. Mak, T. Harko, “Quark stars admitting a one-parameter group of conformal motions”, Internat. J. Modern Phys. D, 13:1 (2004), 149–156, arXiv: gr-qc/0309069 | DOI

[14] M. Chaisi, S. D. Maharaj, “Compact anisotropic spheres with prescribed energy density”, Gen. Rel. Grav., 37:7 (2005), 1177–1189, arXiv: gr-qc/0504098 | DOI | MR

[15] M. Kalam, F. Rahaman, S. Ray, S. M. Hossein, I. Karar, J. Naskar, “Anisotropic strange star with de Sitter spacetime”, Eur. Phys. J. C, 72:12 (2012), 2248, 7 pp., arXiv: 1201.5234 | DOI

[16] M. Kalam, F. Rahaman, S. M. Hossein, S. Ray, “Central density dependent anisotropic compact stars”, Eur. Phys. J. C, 73:4 (2013), 2409, 6 pp., arXiv: 1301.0271 | DOI

[17] V. Fayaz, H. Hossienkhani, A. Aghamohammadi, “Power-law solution for anisotropic universe in $f(G)$ gravity”, Astrophys. Space Sci., 357:2 (2015), 136, 9 pp. | DOI

[18] M. Sharif, H. I. Fatima, “Noncommutative wormhole solutions in $f(G)$ gravity”, Mod. Phys. Lett. A, 30:28 (2015), 1550142 | DOI | MR

[19] M. Zubair, G. Abbas, I. Noureen, “Possible formation of compact stars in $f(R,T)$ gravity”, Astrophys. Space Sci., 361:1 (2016), 8, 10 pp. | DOI | MR

[20] G. Abbas, D. Momeni, M. A. Ali, R. Myrzakulov, S. Qaisar, “Anisotropic compact stars in $f(G)$ gravity”, Astrophys. Space Sci., 357:2 (2015), 158, 11 pp. | DOI

[21] G. Abbas, S. Nazeer, M. A. Meraj, “Cylindrically symmetric models of anisotropic compact stars”, Astrophys. Space Sci., 354:2 (2014), 449–455 | DOI

[22] G. Abbas, A. A. Kanwal, M. Zubair, “Anisotropic compact stars in $f(T)$ gravity”, Astrophys. Space Sci., 357:2 (2015), 109, 8 pp. | DOI

[23] M. Camenzind, Compact Objects in Astrophysics. White Dwarfs, Neutron Stars and Black Holes, Springer, Berlin, 2007 | DOI

[24] R. Goswami, A. M. Nzioki, S. D. Maharaj, S. G. Ghosh, “Collapsing spherical stars in $f(R)$ gravity”, Phys. Rev. D, 90:8 (2014), 084011, 10 pp., arXiv: 1409.2371 | DOI

[25] A. V. Astashenok, S. Capozziello, S. D. Odintsov, “Extreme neutron stars from extended theories of gravity”, J. Cosmol. Astropart. Phys., 2015:1 (2015), 001, 19 pp. | DOI | MR

[26] A. V. Astashenok, S. Capozziello, S. D. Odintsov, “Nonperturbative models of quark stars in $f(R)$ gravity”, Phys. Lett. B, 742 (2015), 160–166, arXiv: 1412.5453 | DOI

[27] D. Momeni, P. H. R. S. Moraes, H. Gholizade, R. Myrzakulov, “Mimetic compact stars”, Internat. J. Geom. Meth. Modern Phys, 15:6 (2018), 1850091, 19 pp. | DOI | MR

[28] D. Momeni, H. Gholizade, M. Raza, R. Myrzakulov, “Tolman–Oppenheimer–Volkoff equations in nonlocal $f(R)$ gravity”, Internat. J. Modern Phys. A, 30:16 (2015), 1550093, 20 pp., arXiv: 1502.05000 | DOI | MR

[29] S. Capozziello, M. De Laurentis, R. Farinelli, S. D. Odintsov, “Mass-radius relation for neutron stars in $f(R)$ gravity”, Phys. Rev. D, 93:2 (2016), 023501, 11 pp. | DOI | MR

[30] A. V. Astashenok, S. Capozziello, S. D. Odintsov, “Maximal neutron star mass and the resolution of the hyperon puzzle in modified gravity”, Phys. Rev. D, 89:10 (2014), 103509, 8 pp., arXiv: 1401.4546 | DOI

[31] N. Itoh, “Hydrostatic equilibrium of hypothetical quark stars”, Prog. Theor. Phys., 44:1 (1970), 291–292 | DOI

[32] E. Farhi, R. L. Jaffe, “Strange matter”, Phys. Rev. D, 30:11 (1984), 2379–2390 | DOI

[33] C. Alcock, E. Farhi, A. Olinto, “Strange stars”, Astrophys. J., 310 (1986), 261–272 | DOI

[34] P. Haensel, J. L. Zdunik, R. Schaefer, “Strange quark stars”, Astron. Astrophys., 160:1 (1986), 121–128

[35] B. V. Ivanov, “Maximum bounds on the surface redshift of anisotropic stars”, Phys. Rev. D, 65:10 (2002), 104011, 4 pp., arXiv: gr-qc/0201090 | DOI | MR

[36] M. K. Mak, T. Harko, “Anisotropic stars in general relativity”, Proc. Roy. Soc. London Ser. A, 459:2030 (2003), 393–408, arXiv: gr-qc/0110103 | DOI | MR

[37] M. Gleiser, K. Dev, “Anistropic stars: Exact solutions and stability”, Internat. J. Modern Phys. D, 13:7 (2004), 1389–1397, arXiv: astro-ph/0401546 | DOI

[38] M. K. Jasim, “Anisotropic strange stars in Tolman–Kuchowicz spacetime”, Eur. Phys. J. C, 78:7 (2018), 603, 11 pp., arXiv: 1801.10594 | DOI

[39] S. K. Maurya, F. Tello-Ortiz, “Generalized relativistic anisotropic compact star models by gravitational decoupling”, Eur. Phys. J. C, 79 (2019), 85, 79–85, 14 pp. | DOI

[40] D. Deb, S. R. Chowdhury, S. Ray, F. Rahaman, B. K. Guha, “Relativistic model for anisotropic strange stars”, Ann. Phys., 387 (2017), 239–252, arXiv: 1606.00713 | DOI | MR

[41] S. Biswas, D. Shee, S. Ray, F. Rahaman, B. K. Guha, “Relativistic strange stars in Tolman–Kuchowicz spacetime”, Ann. Phys., 409 (2019), 167905, 19 pp. | DOI | MR

[42] R. C. Tolman, “Static solutions of Einstein's field equations for spheres of fluid”, Phys. Rev., 55:4 (1939), 364–373 | DOI

[43] B. Kuchowicz, “General relativistic fluid spheres. I. New solutions for spherically symmetric matter distributions”, Acta Phys. Pol., 33 (1968), 541–563

[44] G. J. Olmo, D. R. Garcia, A. Wojnar, “Stellar structure models in modified theories of gravity: lessons and challenges”, Phys. Rep., 876 (2020), 1–75, arXiv: 1912.05202 | DOI | MR

[45] M. F. Shamir, T. Naz, “Stellar structures in $f(\mathcal G)$ gravity with Tolman–Kuchowicz spacetime”, Phys. Dark Universe, 27 (2020), 100472, 11 pp. | DOI

[46] K. D. Krori, J. Barua, “A singularity-free solution for a charged fluid sphere in general relativity”, J. Phys. A: Math. Gen., 8:4 (1975), 508–511 | DOI

[47] A. De Felice, S. Tsujikawa, “Construction of cosmologically viable $f(\mathcal{G})$ gravity models”, Phys. Lett. B, 675:1 (2009), 1–8, arXiv: 0810.5712 | DOI

[48] K. Bamba, S. D. Odintsov, L. Sebastiani, S. Zerbini, “Finite-time future singularities in modified Gauss–Bonnet and $\mathscr F(R,G)$ gravity and singularity avoidance”, Eur. Phys. J. C, 67 (2010), 295–310 | DOI | MR

[49] S. Nojiri, S. D. Odintsov, P. V. Tretyakov, “From inflation to dark energy in the non-minimal modified gravity”, Prog. Theor. Phys. Suppl., 172 (2008), 81–89, arXiv: 0710.5232 | DOI

[50] H. J. Schmidt, “Gauss–Bonnet lagrangian $G\ln G$ and cosmological exact solutions”, Phys. Rev. D, 83:8 (2011), 083513, 7 pp., arXiv: gr-qc/0407053 | DOI

[51] V. Faraoni, “Jebsen–Birkhoff theorem in alternative gravity”, Phys. Rev. D, 81:4 (2010), 044002, 10 pp., arXiv: 1001.2287 | DOI | MR

[52] J. R. Oppenheimer, G. M. Volkoff, “On massive neutron cores”, Phys. Rev., 55:4 (1939), 374–381 | DOI

[53] L. Herrera, “Cracking of self-gravitating compact objects”, Phys. Lett. A, 165:3 (1992), 206–210 | DOI

[54] S. K. Maurya, “Relativistic modeling of compact stars for anisotropic matter distribution”, Eur. Phys. J. A, 53 (2017), 89, 11 pp. | DOI

[55] P. H. R. S. Moraes, J. D. V. Arbañil, M. Malheiro, “Stellar equilibrium configurations of compact stars in $f(R,T)$ theory of gravity”, J. Cosmol. Astropart. Phys., 2016:6 (2016), 005, 12 pp. | DOI | MR

[56] G. A. Carvalho, R. V. Lobato, P. H. R. S. Moraes, J. D. V. Arbañil, E. Otoniel, R. M. Marinho, Jr., M. Malheiro, “Stellar equilibrium configurations of white dwarfs in the $f(R, T)$ gravity”, Eur. Phys. J. C, 77 (2017), 871, 8 pp. | DOI

[57] A. V. Astashenok, S. D. Odintsov, Á. de la Cruz-Dombriz, “The realistic models of relativistic stars in $f(R)=R+\alpha R^2$ gravity”, Class. Quantum Grav., 34:20 (2017), 205008, 20 pp., arXiv: 1704.08311 | DOI | MR

[58] A. V. Astashenok, S. Capozziello, S. D. Odintsov, “Further stable neutron star models from $f(R)$ gravity”, JCAP, 2013:12 (2013), 040, arXiv: 1309.1978 | DOI

[59] S. Ray, A. L. Espíndola, M. Malheiro, J. P. S. Lemos, V. T. Zanchin, “Electrically charged compact stars and formation of charged black holes”, Phys. Rev. D, 68:8 (2003), 084004, 10 pp., arXiv: astro-ph/0307262 | DOI

[60] J. D. V. Arbañil, J. P. S. Lemos, V. T. Zanchin, “Polytropic spheres with electric charge: compact stars, the Oppenheimer–Volkoff and Buchdahl limits, and quasiblack holes”, Phys. Rev. D, 88:8 (2013), 084023, 16 pp., arXiv: 1309.4470 | DOI

[61] E. Witten, “Cosmic separation of phases”, Phys. Rev. D, 30:2 (1984), 272–285 | DOI

[62] N. Stergioulas, “Rotating stars in relativity”, Living Rev. Relativ., 6 (2003), 2003-3, 109 pp., arXiv: gr-qc/0302034 | DOI | MR

[63] J. D. V. Arbañil, M. Malheiro, “Equilibrium and stability of charged strange quark stars”, Phys. Rev. D, 92:8 (2015), 084009, 11 pp., arXiv: 1509.07692 | DOI

[64] R. P. Negreiros, F. Weber, M. Malheiro, V. Usov, “Electrically charged strange quark stars”, Phys. Rev. D, 80:8 (2009), 083006, 6 pp., arXiv: 0907.5537 | DOI

[65] M. F. Shamir, M. Ahmad, “Stellar hydrostatic equilibrium compact structures in $f(\mathscr G,T)$ gravity”, Modern Phys. Lett. A, 34:5 (2019), 1950038, 17 pp., arXiv: 1807.09103 | DOI | MR