Geodesic
Effect of $f(R)$-gravity models on compact stars
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 1, pp. 126-142 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the possibility of forming anisotropic compact stars in the framework of $f(R)$-modified gravity in a static spherically symmetric space–time. We find the unknown coefficients involved in the metric using masses and radii of the compact stars 4U 1820-30, Cen X-3, EXO 1785-248, and LMC X-4. We obtain the hydrostatic equilibrium equation for different forces and use the generalized Tolman–Oppenheimer–Volkoff equation to analyze the behavior of stars. Moreover, we verify the regularity conditions, anisotropic behavior, energy conditions, and stability of the compact stars. We use the effective energy–momentum tensor in $f(R)$ gravity for the analysis. We show that in the framework of $f(R)$ gravity theory, these compact stars have physically acceptable patterns. Our results here also agree with those in general relativity, which is a special case of $f(R)$ gravity.
Mots-clés : anisotropic fluid
Keywords: $f(R)$ gravity, compact star. 
@article{TMF_2020_202_1_a9,
     author = {M. F. Shamir and I. Fayyaz},
     title = {Effect of $f(R)$-gravity models on compact stars},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {126--142},
     year = {2020},
     volume = {202},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_1_a9/}
}
TY  - JOUR
AU  - M. F. Shamir
AU  - I. Fayyaz
TI  - Effect of $f(R)$-gravity models on compact stars
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2020
SP  - 126
EP  - 142
VL  - 202
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2020_202_1_a9/
LA  - ru
ID  - TMF_2020_202_1_a9
ER  - 
%0 Journal Article
%A M. F. Shamir
%A I. Fayyaz
%T Effect of $f(R)$-gravity models on compact stars
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2020
%P 126-142
%V 202
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2020_202_1_a9/
%G ru
%F TMF_2020_202_1_a9
M. F. Shamir; I. Fayyaz. Effect of $f(R)$-gravity models on compact stars. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 1, pp. 126-142. http://geodesic.mathdoc.fr/item/TMF_2020_202_1_a9/

[1] K. Schwarzschild, “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, Königlich Preussische Akademie der Wissenschaften, Berlin, 1916, 189–196; “On the gravitational field of a mass point according to Einstein's theory”, Gen. Rel. Grav., 35:5 (2003), 951–959 | MR

[2] 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

[3] S. K. Maurya, S. D. Maharaj, “Anisotropic fluid spheres of embedding class one using Karmarkar condition”, Eur. Phys. J. C, 77:5 (2017), 328, 13 pp., arXiv: 1702.04192 | DOI

[4] R. L. Bowers, E. P. T. Liang, “Anisotropic spheres in general relativity”, Astrophys. J., 188 (1974), 657–665 | DOI

[5] R. Ruderman, “Pulsars: structure and dynamics”, Ann. Rev. Astron. Astrophys., 10 (1972), 427–476 | DOI

[6] M. F. Shamir, M. Ahmad, “Some exact solutions in $f(\mathcal{G},T)$ gravity via Noether symmetries”, Modern Phys. Lett. A, 32:16, 1750086, 16 pp. | DOI | MR

[7] M. F. Shamir, M. Ahmad, “Noether symmetry approach in $f(\mathcal{G},T)$ gravity”, Eur. Phys. J. C, 77 (2017), 55, 6 pp., arXiv: 1611.07338 | DOI

[8] B. Li, T. P. Sotiriou, J. B. Barrow, “$f(T)$ gravity and local Lorentz invariance”, Phys. Rev. D, 83:6 (2011), 064035, 5 pp., arXiv: 1010.1041 | DOI

[9] T. Harko, F. S. N. Lobo, S. Nojiri, S. D. Odintsov, “$f(R,T)$ gravity”, Phys. Rev. D, 84:2 (2011), 024020, 11 pp., arXiv: 1104.2669 | DOI

[10] S. Capozziello, De M. Laurentis, S. D. Odintsov, A. Stabile, “Hydrostatic equilibrium and stellar structure in $f(R)$-gravity”, Phys. Rev. D, 83:6 (2011), 064004, 6 pp., arXiv: 1101.0219 | DOI

[11] 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

[12] S. Nojiri, S. D. Odintsov, “Modified $f(R)$ gravity consistent with realistic cosmology: from a matter dominated epoch to a dark energy universe”, Phys. Rev. D, 74:8 (2006), 086005, 13 pp., arXiv: hep-th/0608008 | DOI

[13] D. Lovelock, “The Einstein tensor and its generalizations”, J. Math. Phys., 12:3 (1971), 498–501 | DOI | MR

[14] T. Harko, “Evolution of cosmological perturbations in Bose–Einstein condensate dark matter”, Mon. Not. R. Astron. Soc., 413:4 (2011), 3095–3104, arXiv: 1101.3655 | DOI

[15] M. F. Shamir, T. Naz, “Kompaktnye zvezdy s modifitsirovannym uravneniem Tolmana–Oppengeimera–Volkova v teorii gravitatsii Gaussa–Bonne”, ZhETF, 155:6 (2019), 1029–1036 | DOI

[16] 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

[17] M. Sharif, A. Ikram, “Warm inflation in $f(\mathcal G)$ theory of gravity”, ZhETF, 150:1 (2016), 48–59 | DOI

[18] S. Capozziello, S. Nojiri, D. Odintsov, A. Troisi, “Cosmological viability of $f(R)$-gravity as an ideal fluid and its compatibility with a matter dominated phase”, Phys. Lett. B, 639:3–4 (2006), 135–143, arXiv: astro-ph/0604431 | DOI

[19] L. Amendola, D. Polarski, S. Tsujikawa, “Power-laws $f(R)$ theories are cosmologically unacceptable”, Internat. J. Modern Phys. D, 16:10 (2007), 1555–1561, arXiv: astro-ph/0605384 | DOI

[20] L. Amendola, D. Polarski, S. Tsujikawa, “Are $f(R)$ dark energy models cosmologically viable?”, Phys. Rev. Lett., 98:13 (2007), 131302, 4 pp. | DOI | MR

[21] J. Santos, J. S. Alcaniz, “Energy conditions and Segre classification of phantom fields”, Phys. Lett. B, 619:1–2 (2005), 11–16 | DOI

[22] S. M. Carroll, M. Hoffman, M. Trodden, “Can the dark energy equation-of-state parameter $w$ be less than $-1$?”, Phys. Rev. D, 68:2 (2003), 023509, 11 pp. | DOI

[23] J. S. Alcaniz, “Testing dark energy beyond the cosmological constant barrier”, Phys. Rev. D, 69:8 (2004), 083521, 5 pp., arXiv: astro-ph/0312424 | DOI

[24] J. D. Barrow, S. Hervik, “Anisotropically inflating universes”, Phys. Rev. D, 73:2 (2006), 023007, 5 pp. | DOI | MR

[25] M. Visser, “Energy conditions in the epoch of galaxy formation”, Science, 276:5309 (1997), 88–90, arXiv: 1501.01619 | DOI

[26] J. Santos, J. S. Alcaniz, M. J. Rebouças, “Energy conditions and supernovae observations”, Phys. Rev. D, 74:6 (2006), 067301, 4 pp. | DOI

[27] J. Santos, J. S. Alcaniz, M. J. Rebouças, N. Pires, “Lookback time bounds from energy conditions”, Phys. Rev. D, 76:4 (2007), 043519, 7 pp., arXiv: 0706.1779 | DOI

[28] M. J. Rebouças, J. Santos, “Gödel-type universes in $f(R)$ gravity”, Phys. Rev. D, 80:6 (2009), 063009, 7 pp. | DOI

[29] J. Santos, M. J. Rebouças, T. B. R. F. Oliveira, “Gödel-type universes in Palatini $f(R)$ gravity”, Phys. Rev. D, 81:12 (2010), 123017, 7 pp., arXiv: 1004.2501 | DOI | MR

[30] J. Wang, Y.-B. Wu, Y.-X. Guo, W.-Q. Yang, L. Wang, “Energy conditions and stability in generalized $f(R)$ gravity with arbitrary coupling between matter and geometry”, Phys. Lett. B, 689:4–5 (2010), 133–138, arXiv: 1212.4921 | DOI | MR

[31] K. Atazadeh, “Energy conditions in $f(R)$ gravity and Brans–Dicke theories”, Internat. J. Modern Phys. D, 18:7 (2009), 1101–1111, arXiv: 0811.4269 | DOI | MR

[32] A. Banijamali, B. Fazlpour, M. R. Setare, “Energy conditions in $f(G)$ modified gravity with non-minimal coupling to matter”, Astrophys. Space Sci., 338:2 (2012), 327–332 | DOI

[33] J. Wang, K. Liao, “Energy conditions in $f(R,L_m)$ gravity”, Class. Quantum Grav., 29:21 (2012), 215016, 9 pp. | DOI | MR

[34] S. M. Hossein, F. Rahaman, J. Naskar, M. Kalam, S. Ray, “Anisotropic compact stars with variable cosmological constant”, Internat. J. Modern Phys. D, 21:13 (2012), 1250088, 14 pp., arXiv: 1204.3558 | DOI | Zbl

[35] B. V. Ivanov, “Analytical study of anisotropic compact star models”, Eur. Phys. J. C, 77:11 (2017), 738, 12 pp. | DOI

[36] 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

[37] A. Aziz, S. Ray, F. Rahaman, “A generalized model for compact stars”, Eur. Phys. J. C, 76:5 (2016), 248, 9 pp. | DOI

[38] 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

[39] A. V. Astashenok, S. D. Odintsov, “From neutron stars to quark stars in mimetic gravity”, Phys. Rev. D, 94:6 (2016), 063008, 12 pp., arXiv: 1512.07279 | DOI

[40] A. V. Astashenok, S. Capozziello, S. D. Odintsov, “Magnetic neutron stars in $f(R)$ gravity”, Astrophys. Space Sci., 355:2 (2015), 333–341 | DOI

[41] M. Zubair, G. Abbas, Study of anisotropic compact stars in Starobinsky model, arXiv: 1412.2120

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

[43] 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

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

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

[46] G. K. Patwardhan, P. C. Vaidya, “Relativistic distributions of matter of radial symmetry”, J. Univ. Bombay (N. S.), 12:3 (1943), 23–36 | MR | Zbl

[47] A. L. Mehra, “Radially symmetric distribution of matter”, J. Austr. Math. Soc., 6:2 (1966), 153–155 | DOI

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

[49] C. Leibovitz, “Spherically symmetric static solutions of Einstein's equations”, Phys. Rev. D, 185:5 (1969), 1664–1669 | DOI | MR

[50] S. K. Maurya, Y. K. Gupta, S. Ray, B. Dayanandan, “Anisotropic models for compact stars”, Eur. Phys. J. C, 75:5 (2015), 225, 11 pp., arXiv: 1504.00209 | DOI

[51] A. A. Starobinsky, “A new type of isotropic cosmological models without singularity”, Phys. Lett. B, 91:1 (1980), 99–102 | DOI

[52] G. Cognola, “Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion”, Phys. Rev. D, 77:4 (2008), 046009, 11 pp. | DOI

[53] T. Clifton, “Further exact cosmological solutions to higher-order gravity theories”, Class. Quantum Grav., 23:24 (2006), 7445–7454, arXiv: gr-qc/0607096 | DOI

[54] A. Ganguly, R. Gannouji, R. Goswami, S. Ray, “Neutron stars in the Starobinsky model”, Phys. Rev. D, 89:6 (2014), 064019, 11 pp. | DOI

[55] A. Cooney, S. DeDeo, D. Psaltis, “Neutron stars in $f(R)$ gravity with perturbative constraints”, Phys. Rev. D, 82:6 (2010), 064033, 7 pp. | DOI

[56] D. Momeni, R. Myrzakulov, “Tolman–Oppenheimer–Volkoff equations in modified Gauss–Bonnet gravity”, Internat. J. Geom. Methods Modern Phys., 12:2 (2015), 1550014, 8 pp. | DOI | MR

[57] H. Stephani, General Relativity, Cambridge Univ. Press, Cambridge, 1990 | MR

[58] T. Güver, P. Wroblewski, L. Camarota, F. Özel, “The mass and radius of the neutron star in 4U 1820-30”, Astrophys. J., 719:2 (2010), 1807–1812, arXiv: 1002.3825 | DOI

[59] M. L. Rawls, J. A. Orosz, J. E. McClintock, M. A. P. Torres, C. D. Bailyn, M. M. Buxton, “Refined neutron star mass determinations for six eclipsing X-ray pulsar binaries”, Astrophys. J., 730:1 (2011), 25, 11 pp. | DOI

[60] F. Özel, T. Güver, T. Psaltis, “The mass and radius of the neutron star in EXO 1745-248”, Astrophys. J., 693:2 (2009), 1775–1789 | DOI

[61] Z. Yousaf, “Stellar filaments with Minkowskian core in the Einstein–$\Lambda$ gravity”, Eur. Phys. J. Plus, 132:6 (2017), 276, 14 pp. | DOI

[62] K. Bamba, M. Ilyas, M. Z. Bhatti, Z. Yousaf, “Energy conditions in modified $f(G)$ gravity”, Gen. Rel. Grav., 49:8 (2017), 112, 17 pp. | DOI | MR

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

[64] H. Abreu, H. Hernández, L. A. Núñez, “Sound speeds, cracking and the stability of self-gravitating anisotropic compact objects”, Class. Quantum Grav., 24:18 (2007), 4631–4645 | DOI | MR