Geodesic
Study on anisotropic strange stars in Rastall gravity
Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 3, pp. 522-543 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The strange quark matter (SQM) whose distribution is governed by the simplified MIT bag model equation of state has been the subject of a series of investigations within the framework of Rastall's theory. We obtain an exact solution of the modified form of the Tolman–Oppenheimer–Volkoff (TOV) equation in the Rastall gravity theory and study the dependence of different physical properties (the total mass, radius, energy density, and pressure) for the chosen values of the Rastall parameter $\lambda_{\scriptscriptstyle{\mathrm{Ras}}}$. To examine physical acceptability of the proposed stellar model, we conduct different tests in detail: the energy conditions, the the mass–radius relation, the Compactification factor, the redshift, the system stability, the modified TOV equation, the causality condition, and the adiabatic index in terms of $\lambda_{\scriptscriptstyle{\mathrm{Ras}}}$. We precisely explain the effects arising due to the Rastall parameter and geometry on the compact stellar system. We find that as the factor $\lambda_{\scriptscriptstyle{\mathrm{Ras}}}$ decreases, the strange star candidates become gradually massive and larger in size with a less dense stellar configuration. But when $\lambda_{\scriptscriptstyle{\mathrm{Ras}}}$ increases, the stars shrink gradually and become less massive, turning into a more compact stellar system. For $\lambda_{\scriptscriptstyle{\mathrm{Ras}}}>0$, our proposed model is therefore suitable for explaining the ultradense compact stars well within the observational limits; for $\lambda_{\scriptscriptstyle{\mathrm{Ras}}}<0$, it allows representing the recent massive pulsars and super-Chandrasekhar stars. For $\lambda_{\scriptscriptstyle{\mathrm{Ras}}}=1$, we retrieve the standard results of general relativity.
Keywords: dark energy theory, Rastall gravity, massive star. 
@article{TMF_2021_208_3_a9,
     author = {I. G. Salako and D. R. Boko and G. F. Pomalegni and M. Z. Arouko},
     title = {Study on anisotropic strange stars in {Rastall} gravity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {522--543},
     year = {2021},
     volume = {208},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a9/}
}
TY  - JOUR
AU  - I. G. Salako
AU  - D. R. Boko
AU  - G. F. Pomalegni
AU  - M. Z. Arouko
TI  - Study on anisotropic strange stars in Rastall gravity
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 522
EP  - 543
VL  - 208
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a9/
LA  - ru
ID  - TMF_2021_208_3_a9
ER  - 
%0 Journal Article
%A I. G. Salako
%A D. R. Boko
%A G. F. Pomalegni
%A M. Z. Arouko
%T Study on anisotropic strange stars in Rastall gravity
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 522-543
%V 208
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a9/
%G ru
%F TMF_2021_208_3_a9
I. G. Salako; D. R. Boko; G. F. Pomalegni; M. Z. Arouko. Study on anisotropic strange stars in Rastall gravity. Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 3, pp. 522-543. http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a9/

[1] A. R. Bodmer, “Collapsed nuclei”, Phys. Rev. D, 4:6 (1971), 1601–1606 | DOI

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

[3] W. Baade, F. Zwicky, “Remarks on super-novae and cosmic rays”, Phys. Rev., 46:1 (1934), 76–77 | DOI

[4] J. M. Lattimer, M. Prakash, “The physics of neutron stars”, Science, 304:5670 (2004), 536–542, arXiv: astro-ph/0405262 | DOI

[5] A. W. Steiner, M. Prakash, J. M. Lattimer, P. J. Ellis, “Isospin asymmetry in nuclei and neutron stars”, Phys. Rep., 411:6 (2005), 325–375, arXiv: nucl-th/0410066 | DOI

[6] I. Bombaci, I. Parenti, I. Vidaña, “Quark deconfinement and implications for the radius and the limiting mass of compact stars”, Astrophys. J., 614:1 (2004), 314–325, arXiv: astro-ph/0402404 | DOI

[7] J. Staff, R. Ouyed, M. Bagchi, “A three-stage model for the inner engine of gamma-ray bursts: prompt emission and early afterglow”, Astrophys. J., 667:1 (2007), 340–350, arXiv: astro-ph/0608470 | DOI

[8] M. Herzog, F. K. Röpke, “Three-dimensional hydrodynamic simulations of the combustion of a neutron star into a quark star”, Phys. Rev. D, 84:8 (2011), 083002, 13 pp., arXiv: 1109.0539 | DOI

[9] K. Schwarzschild, “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.), 7 (1916), 189–196

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

[11] L. Herrera, N. O. Santos, “Local anisotropy in self-gravitating systems”, Phys. Rep., 286:2 (1997), 53–130 | DOI | MR

[12] A. Hewish, S. J. Bell, J. D. H. Pilkington, P. F. Scott, R. A. Collins, “Observation of a rapidly pulsating radio source”, Nature, 217:5130 (1968), 709–713 | DOI

[13] 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

[14] M. Kalam, F. Rahaman, S. Molla, S. M. Hossein, “Anisotropic quintessence stars”, Astrophys. Space Sci., 349:2 (2014), 865–871 | DOI

[15] 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

[16] M. Kalam, F. Rahaman, S. Ray, Sk. 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

[17] B. C. Paul, R. Deb, “Relativistic solutions of anisotropic compact objects”, Astrophys. Space Sci., 354:2 (2014), 421–430 | DOI

[18] K. S. Cheng, Z. G. Dai, T. Lu, “Strange stars and related astrophysical phenomena”, Inernat. J. Modern Phys. D, 7:2 (1998), 139–176 | DOI

[19] P. Bhar, “Singularity-free anisotropic strange quintessence star”, Astrophys. Space Sci., 356:2 (2015), 309–318 | DOI

[20] G. Abbas, M. Zubair, G. Mustafa, “Anisotropic strange quintessence stars in $f(R)$ gravity”, Astrophys. Space Sci., 358:2 (2015), 26, 11 pp. | DOI

[21] L. Lagerkvist, F. Samuelsson, The MIT bag-model: Glueball mass spectrum using the MIT bag-model, Bachelor Thesis in Theoretical Physics, Royal Institute of Technology (KTH), School of Engineering Sciences (SCI), Stockholm, 2015

[22] F. Rahaman, K. Chakraborty, P. K. F. Kuhfittig, G. C. Shit, M. Rahman, “A new deterministic model of strange stars”, Eur. Phys. J. C, 74:10 (2014), 3126, 5 pp. | DOI

[23] J. D. V. Arbañil, M. Malheiro, “Radial stability of anisotropic strange quark stars”, J. Cosmol. Astropart. Phys., 2016:11 (2016), 012, 17 pp. | DOI | MR

[24] M. H. Murad, “Some analytical models of anisotropic strange stars”, Astrophys. Space Sci., 361:1 (2016), 20, 13 pp. | DOI | MR

[25] 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 | DOI

[26] G. Abbas, “Cardy–Verlinde formula of non-commutative Schwarzschild black hole”, Adv. High Energy Phys., 2014 (2014), 306256, 4 pp. | DOI

[27] G. Abbas, “Collapse and expansion of anisotropic plane symmetric source”, Astrophys. Space Sci., 350:1 (2014), 307–311 | DOI

[28] G. Abbas, U. Sabiullah, “Geodesic study of regular Hayward black hole”, Astrophys. Space Sci., 352:2 (2014), 769–774 | DOI

[29] G. Abbas, “Phantom energy accretion onto a black hole in Hor̆ava–Lifshitz gravity”, Sci. China Phys. Mech. Astron., 57:4 (2014), 604–607 | DOI

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

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

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

[33] D. Deb, S. Ghosh, S. K. Maurya, M. Khlopov, S. Ray, “Anisotropic compact stars in $f(T)$ gravity under Karmarkar condition”, Tech Vistas, 1:1 (2018), 1–20, arXiv: 1811.11797

[34] A. Das, S. Ghosh, D. Deb, F. Rahaman, S. Ray, “Study of gravastars under $f(\mathbb{T})$ gravity”, Nucl. Phys. B, 954 (2020), 114986, 17 pp. | DOI | MR

[35] 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

[36] G. Abbas, S. Qaisar, A. Jawad, “Strange stars in $f(T)$ gravity with MIT bag model”, Astrophys. Space Sci., 359:2 (2015), 57, 10 pp. | DOI

[37] A. M. Oliveira, H. E. S. Velten, J. C. Fabris, L. Casarini, “Neutron stars in Rastall gravity”, Phys. Rev. D, 92:4 (2015), 044020, 6 pp., arXiv: 1506.00567 | DOI

[38] G. Abbas, M. R. Shahzad, “A new model of quintessence compact stars in the Rastall theory of gravity”, Eur. Phys. J. A, 54:12 (2018), 211, 11 pp. | DOI

[39] G. Abbas, M. R. Shahzad, “Models of anisotropic compact stars in the Rastall theory of gravity”, Astrophys. Space Sci., 364:3 (2019), 50, 12 pp. | DOI | MR

[40] C. E. Mota, L. C. N. Santos, G. Grams, F. M. da Silva, D. P. Menezes, “Combined Rastall and rainbow theories of gravity with applications to neutron stars”, Phys. Rev. D, 100:2 (2019), 024043, 9 pp., arXiv: 1905.01250 | DOI | MR

[41] C. E. Mota, L. C. N. Santos, F. M. da Silva, C. V. Flores, T. J. N. da Silva, D. P. Menezes, Anisotropic compact stars in Rastall–Rainbow gravity, arXiv: 1911.03208

[42] R. Rizaldy, A. Sulaksono, “Deformation of a magnetized quark star in Rastall gravity”, J. Phys.: Conf. Ser., 1321:2 (2019), 022016, 7 pp. | DOI

[43] M. R. Shahzad, G. Abbas, “Strange stars with MIT bag model in the Rastall theory of gravity”, Internat. J. Geom. Meth. Modern Phys., 16:9 (2019), 1950132, 22 pp. | DOI | MR

[44] H. Nazar, G. Abbas, “Charged anisotropic collapsing stars with heat flux in $f(R)$ gravity”, Chinese J. Phys., 63 (2020), 436–447 | DOI | MR

[45] M. Pace, J. L. Said, “Quark stars in $f(T,\mathcal T)$-gravity”, Eur. Phys. J. C, 77:2 (2017), 62, 5 pp., arXiv: 1701.04761 | DOI

[46] P. Rastall, “Generalization of the Einstein theory”, Phys. Rev. D, 6:12 (1972), 3357–3359 | DOI | MR

[47] P. Rastall, “A theory of gravity”, Canad. J. Phys., 54:1 (1976), 66–75 | DOI | MR

[48] A. S. Al-Rawaf, M. O. Taha, “A resolution of the cosmological age puzzle”, Phys. Lett. B, 366:1–4 (1996), 69–71 | DOI | MR

[49] A. S. Al-Rawaf, M. O. Taha, “Cosmology of general relativity without energy-momentum conservation”, Gen. Rel. Grav., 28:8 (1996), 935–952 | DOI | MR

[50] L. L. Smalley, “Variational principle for a prototype Rastall theory of gravitation”, Nuovo Cim. B, 80:1 (1984), 42–48 | DOI

[51] C. E. M. Batista, J. C. Fabris, M. H. Daouda, “Testing the Rastall's theory using matter power spectrum”, Nuovo Cim. B, 125:8 (2010), 957–968 | DOI

[52] J. C. Fabris, T. C. C. Guio, M. H. Daouda, O. F. Piattella, “Scalar models for the generalized Chaplygin gas and the structure formation constraints”, Gravit. Cosmol., 17:3 (2011), 259–271 | DOI

[53] J. C. Fabris, M. H. Daouda, O. F. Piattella, “Note on the evolution of the gravitational potential in Rastall scalar field theories”, Phys. Lett. B, 711:3–4 (2012), 232–237, arXiv: 1109.2096 | DOI

[54] M. Capone, V. F. Cardone, M. L. Ruggiero, “Accelerating cosmology in Rastall's theory”, Nuovo Cim. B, 125:10 (2011), 1133–1142 | DOI

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

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

[57] A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn, V. F. Weisskopf, “New extended model of hadrons”, Phys. Rev. D, 9:12 (1974), 3471–3495 | DOI | MR

[58] D. Deb, S. V. Ketov, M. Khlopov, S. Ray, “Study on charged strange stars in $f(R,T)$ gravity”, J. Cosmol. Astropart. Phys., 2019:10 (2019), 070, 27 pp. | DOI | MR

[59] J. L. Zdunik, T. Bulik, W. Kluźniak, P. Haensel, D. Gondek-Rosińska, “On the mass of moderately rotating strange stars in the MIT bag model and LMXBs”, Astron. Astrophys., 359:1 (2000), 143–147, arXiv: astro-ph/0004278

[60] C. Maieron, M. Baldo, G. F. Burgio, H.-J. Schulze, “Hybrid stars with the color dielectric and the MIT bag models”, Phys. Rev. D, 70:4 (2004), 043010, 11 pp., arXiv: nucl-th/0404089 | DOI

[61] O. E. Nicotra, M. Baldo, G. F. Burgio, H.-J. Schulze, “Hybrid protoneutron stars with the MIT bag model”, Phys. Rev. D, 74:12 (2006), 123001, 11 pp., arXiv: astro-ph/0608021 | DOI

[62] T. Bao, G.-Z. Liu, M.-F. Zhu, “Properties of hybrid stars in an extended MIT bag model”, Chinese Phys. C, 33:5 (2009), 340–344 | DOI

[63] S. T. Uechi, H. Uechi, Hardon-quark hybrid stars constructed by the nonlinear $\sigma$-$\omega$-$\rho$ mean-field model and MIT-bag model, arXiv: 1003.4815

[64] A. A. Isayev, “Stability of magnetized strange quark matter in the MIT bag model with a density dependent bag pressure”, Phys. Rev. C, 91:1 (2015), 015208, 6 pp., arXiv: 1501.07772 | DOI

[65] P. H. G. Cardoso, T. N. da Silva, A. Deppman, D. P. Menezes, “Quark matter revisited with non-extensive MIT bag model”, Eur. Phys. J. A, 53:10 (2017), 191, 8 pp., arXiv: 1706.02183 | DOI

[66] S. Joshi, S. Sau, S. Sanyal, Quark cores in extensions of the MIT bag model, arXiv: 2002.07647

[67] 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

[68] P. H. R. S. Moraes, R. A. C. Correa, R. V. Lobato, “Analytical general solutions for static wormholes in $f(R,T)$ gravity”, J. Cosmol. Astropart. Phys., 2017:7 (2017), 029, 12 pp. | DOI | MR

[69] D. Deb, F. Rahaman, S. Ray, B. K. Guha, “Strange stars in $f(R,\mathcal T)$ gravity”, J. Cosmol. Astropart. Phys., 2018:03 (2018), 044, 22 pp. | DOI

[70] S. K. Maurya, Y. K. Gupta, S. Ray, D. Deb, “Generalised model for anisotropic compact stars”, Eur. Phys. J. C, 76:12 (2016), 693, 12 pp., arXiv: 1607.05582 | DOI

[71] J. P. de Leon, “Limiting configurations allowed by the energy conditions”, Gen. Rel. Grav., 25:11 (1993), 1123–1137 | DOI | MR

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

[73] 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), 4631–4646, arXiv: 0706.3452 | DOI | MR

[74] S. Chandrasekhar, “The dynamical instability of gaseous masses approaching the Schwarzschild limit in general relativity”, Astrophys. J., 140 (1964), 417–433 | DOI | MR

[75] H. Heintzmann, W. Hillebrandt, “Neutron stars with an anisotropic equation of state: mass, redshift and stability”, Astron. Astrophys., 38:1 (1975), 51–55

[76] W. Hillebrandt, K. O. Steinmetz, “Anisotropic neutron star models: stability against radial and nonradial pulsations”, Astron. Astrophys., 53:2 (1976), 283–287

[77] I. Bombaci, “The maximum mass of a neutron star”, Astron. Astrophys., 305 (1996), 871–877

[78] S. Biswas, D. Shee, S. Ray, B. K. Guha, “Anisotropic strange star with Tolman–Kuchowicz metric under $f(R,T)$ gravity”, Eur. Phys. J. C, 80:2 (2020), 175, 15 pp., arXiv: 2006.01619 | DOI

[79] H. A. Buchdahl, “General relativistic fluid spheres”, Phys. Rev., 116:4 (1959), 1027–1034 | DOI | MR

[80] H. Andréasson, “Sharp bounds on the critical stability radius for relativistic charged spheres”, Commun. Math. Phys., 288:2 (2009), 715–730, arXiv: 0804.1882 | DOI | MR

[81] H. Bondi, “The contraction of gravitating spheres”, Proc. Roy. Soc. London Ser. A, 281:1384 (1964), 39–48 | DOI | MR

[82] R. Chan, L. Herrera, N. O. Santos, “Dynamical instability for radiating anisotropic collapse”, Mon. Not. Roy. Astron. Soc., 265:3 (1993), 533–544 | DOI

[83] D. E. Barraco, V. H. Hamity, “Maximum mass of a spherically symmetric isotropic star”, Phys. Rev. D., 65:12 (2002), 124028, 5 pp. | DOI

[84] C. G. Böhmer, T. Harko, “Bounds on the basic physical parameters for anisotropic compact general relativistic objects”, Class. Quantum Grav., 23:22 (2006), 6479–6491, arXiv: gr-qc/0609061 | DOI | MR

[85] 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

[86] A. Aziz, S. Ray, F. Rahaman, M. Khlopov, B. K. Guha, “Constraining values of bag constant for strange star candidates”, Internat. J. Modern Phys. D, 28:13 (2019), 1941006, 22 pp., arXiv: 1906.00063 | DOI

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

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

[89] C. Alcock, E. Farhi, A. Olinto, “Strange stars”, Astrophys. J., 310:1 (1986), 261–272 | DOI

[90] G. Pagliara, M. Herzog, F. K. Röpke, “Combustion of a neutron star into a strange quark star: The neutrino signal”, Phys. Rev. D, 87:10 (2013), 103007, 8 pp., arXiv: 1304.6884 | DOI

[91] A. Bauswein, H.-T. Janka, R. Oechslin, G. Pagliara, I. Sagert, J. Schaffner-Bielich, M. M. Hohle, R. Neuhäuser, “Mass ejection by strange star mergers and observational implications”, Phys. Rev. Lett., 103:1 (2009), 011101, 4 pp., arXiv: 0812.4248 | DOI

[92] A. Bauswein, R. Oechslin, H.-T. Janka, “Discriminating strange star mergers from neutron star mergers by gravitational-wave measurements”, Phys. Rev. D, 81:2 (2010), 024012, 21 pp., arXiv: 0910.5169 | DOI

[93] P. J. Llanes-Estrada, “Constraining gravity with hadron physics: neutron stars, modified gravity and gravitational waves”, EPJ Web Conf., 137 (2017), 01013, 14 pp. | DOI

[94] H. Motohashi, M. Minamitsuji, “General Relativity solutions in modified gravity”, Phys. Lett. B, 781 (2018), 728–734, arXiv: 1804.01731 | DOI