Charged anisotropic collapsing stars with heat flux in \(f(R)\) gravity. (English) Zbl 07829587
Summary: In the present article, we have studied the effects of electromagnetic field on the conformally flat collapsing stars with anisotropic heat conducting fluid in the framework of modified \(f(R)\) theory of gravity. For this purpose, we have formulated the junction conditions between the Vaidya spacetime and interior manifold at the junction interface for the extraction of an exact collapsing solution and the continuity of scalar curvature. Thereafter the physical parameters such as pressures \(P_r\) and \(P_t\), energy density and heat flux are elucidated in the presence of electric charge through graphical representation. Also, we have investigated the different energy conditions for the physical viability of the system. It is found that the presence of charge, divergence of a non-zero acceleration and heat flux diminishes the rate of collapse and settle down the system in a zero volume.
MSC:
| 83Cxx | General relativity |
| 83Dxx | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83Fxx | Relativistic cosmology |
References:
| [1] | Pietrobon, D.; Balbi, A.; Marinucci, D., Integrated Sachs-Wolfe effect from the cross correlation of WMAP3 year and the NRAO VLA sky survey data: New results and constraints on dark energy, Phys. Rev. D, 74, 1-9, (2006), 043524 |
| [2] | Giannantonio, T.; Crittenden, R. G.; Nichol, R. C.; Scranton, R.; Richards, G. T.; Myers, A. D.; Brunner, R. J.; Gray, A. G.; Connolly, A. J.; Schneider, D. P., High redshift detection of the integrated Sachs-Wolfe effect, Phys. Rev. D, 74, 1-10, (2006), 063520 |
| [3] | Riess, A. G., New Hubble Space Telescope Discoveries of Type Ia Supernovae at z >1: Narrowing Constraints on the Early Behavior of Dark Energy, Astrophys. J., 659, 98-121, (2007) |
| [4] | Starobinsky, A. A., A new type of isotropic cosmological models without singularity, Phys. Lett. B, 91, 99-102, (1980) · Zbl 1371.83222 |
| [5] | Kazanas, D., Dynamics of the Universe and Spontaneous Symmetry Breaking, Astrophys. J., 241, L59-L63, (1980) |
| [6] | Guth, A. H., Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D, 23, 347-356, (1981) · Zbl 1371.83202 |
| [7] | Sato, K., First-order phase transition of a vacuum and the expansion of the Universe, Mon. Not. Royal Astron. Soc., 195, 467-479, (1981) |
| [8] | Lyth, D. H.; Riotto, A., Particle Physics Models of Inflation and the Cosmological Density Perturbation, Phys. Rep., 314, 1-146, (1999) |
| [9] | Bassett, B. A.; Tsujikawa, S.; Wands, D., Inflation Dynamics and Reheating, Rev. Mod. Phys., 78, 537-589, (2006) |
| [10] | Sahni, V.; Starobinsky, A. A., The Case for a Positive Cosmological Lambda-term, Int. J. Mod. Phys. D, 09, 373-444, (2000), S.M. Carroll, The Cosmological Constant, Living Rev. Relativity 4 (2001) 1-56; T. Padmanabhan, Cosmological Constant-the Weight of the Vacuum, Phys. Rep. 380 (2003) 235-320; S. Nojiri, S.D. Odintsov, Introduction to Modified Gravity and Gravitational Alternative for Dark Energy, Int. J. Geom. Methods. Mod. Phys. 04 (2007) 115-146 |
| [11] | Copeland, E. J.; Sami, M.; Tsujikawa, S., Dynamics of dark energy, Int. J. Mod. Phys. D, 15, 1753-1936, (2006) · Zbl 1203.83061 |
| [12] | Briscese, F.; Elizalde, E.; Nojiri, S.; Odintsov, S. D., Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity, Phys. Lett. B, 646, 105-111, (2007) |
| [13] | Bamba, K.; Geng, C-Q.; Nojiri, S.; Odintsov, S. D., Crossing of the phantom divide in modified gravity, Phys. Rev. D, 79, 1-15, (2009), 083014 |
| [14] | Capozziello, S., Curvature Quintessence, Int. J. Mod. Phys. D, 11, 483-492, (2002), M. Sharif, H.R. Kausar, Effects of f(R) Dark Energy on Dissipative Anisotropic Collapsing Fluid, Mod. Phys. Lett. A 25 (2010) 3299-3311; Anisotropic fluid and Bianchi type III model in f(R) gravity, Phys. Lett. B 697 (2011) 1-6 · Zbl 1062.83565 |
| [15] | Clifton, T.; Ferreira, P. G.; Padilla, A.; Skordis, C., Modified Gravity and Cosmology, Phys. Rep., 513, 1-189, (2012) |
| [16] | Sotiriou, T. P.; Faraoni, V., f(R) theories of gravity, Rev. Mod. Phys., 82, 451-497, (2010) · Zbl 1205.83006 |
| [17] | Nojiri, S.; Odintsov, S. D., Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models, Phys. Rep., 505, 59-144, (2011) |
| [18] | Nojiri, S.; Odintsov, S. D.; Oikonomou, V. K., Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution, Phys. Rep., 692, 1-104, (2017) · Zbl 1370.83084 |
| [19] | Cognola, G.; Elizalde, E.; Nojiri, S.; Odintsov, S. D.; Sebastiani, L.; Zerbini, S., Class of viable modified f(R) gravities describing inflation and the onset of accelerated expansion, Phys. Rev. D, 77, 1-11, (2008), 046009 |
| [20] | Datt, B., Über eine Klasse von Lösungen der Gravitationsgleichungen der Relativität, Z. Phys., 108, 314-321, (1938) · Zbl 0018.18606 |
| [21] | Oppenheimer, J. R.; Snyder, H. S., On Continued Gravitational Contraction, Phys. Rev., 56, 455-459, (1939) · Zbl 0022.28104 |
| [22] | Misner, C. W.; Sharp, D. H., Relativistic Equations for Adiabatic, Spherically Symmetric Gravitational Collapse, Phys. Rev., 136, B571-B576, (1964) · Zbl 0129.41102 |
| [23] | Vaidya, P. C., The gravitational field of a radiating star, Proc. Indian Acad. Sci. (Math. Sci.) A, 33, 264-276, (1951) · Zbl 0044.42202 |
| [24] | Markovic, D.; Shapiro, S. L., Gravitational collapse with a cosmological constant, Phys. Rev. D, 61, 1-7, (2000), 084029 |
| [25] | Penrose, R.; Hawking, S. W.; Isreal, W., General Relativity, An Einstein Centenary Survey, (1979), Cambridge University Press: Cambridge University Press Cambridge, England · Zbl 0424.53001 |
| [26] | Joshi, P. S., Global Aspects in Gravitation and Cosmology, (1993), Clarendon Press, Oxford University Press: Clarendon Press, Oxford University Press Oxford · Zbl 0853.53055 |
| [27] | Joshi, P. S., Gravitational collapse: The story so far, Pramana - J Phys, 55, 529-544, (2000) |
| [28] | Rosseland, S., Electrical state of a star, Mon. Not. R. Astron. Soc., 84, 720-728, (1924) |
| [29] | Ray, S.; Esp´indola, A. L.; Malheiro, M.; Lemos, J. P.S.; Zanchin, V. T., Electrically charged compact stars and formation of charged black holes, Phys. Rev. D, 68, 1-10, (2003), 084004; C.R. Ghezzi, Relativistic structure, stability, and gravitational collapse of charged neutron stars, Phys. Rev. D 72 (2005) 1-21 104017 |
| [30] | Thirukkanesh, S.; Maharaj, S. D., Charged anisotropic matter with a linear equation of state, Classical Quantum Gravity, 25, 1-14, (2008), 235001 · Zbl 1155.83320 |
| [31] | Esculpi, M.; Aloma, E., Conformal anisotropic relativistic charged fluid spheres with a linear equation of state, Eur. Phys. J. C, 67, 521-532, (2010) |
| [32] | Eiroa, E. F.; Simeone, C., Stability of charged thin shells,Phys, Rev. D, 83, 1-6, (2011), 104009 |
| [33] | Pinheiro, G.; Chan, R., Radiating shear-free gravitational collapse with charge, Gen. Relativ. Gravit., 45, 243-261, (2013) · Zbl 1260.83025 |
| [34] | Bamba, K.; Nojiri, S.; Odintsov, S. D., Time-dependent matter instability and star singularity in F(R) gravity, Phys. Lett. B, 698, 451-456, (2011) |
| [35] | Arbuzova, E. V.; Dolgov, A. D., Explosive phenomena in modified gravity, Phys. Lett. B, 700, 289-293, (2011) |
| [36] | Borisov, A.; Jain, B.; Zhang, P., Spherical collapse in f(R) gravity, Phys. Rev. D, 85, 1-10, (2012), 063518 |
| [37] | Guo, J-Q.; Wang, D.; Frolov, A. V., Spherical collapse in f(R) gravity and the Belinskii-Khalatnikov-Lifshitz conjecture, Phys. Rev. D, 90, 1-26, (2014), 024017 |
| [38] | Cembranos, J. A.R.; de la Cruz-Dombriz, A.; Montes-Nu˜nez, B., Gravitational collapse in f(R) theories, J, Cosmol. Astropart. Phys., 04, 1-18, (2012), 021 |
| [39] | Sharif, M.; Yousaf, Z., Effects of CDTT model on the stability of spherical collapse in Palatini f(R) gravity, Eur. Phys. J. C, 73, 1-12, (2013), 2633 |
| [40] | Kausar, H. R.; Noureen, I., Dissipative spherical collapse of charged anisotropic fluid in f(R) gravity, Eur. Phys. J. C, 74, 1-8, (2014), 2760 |
| [41] | Israel, W., Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B, 44, 1-14, (1966) |
| [42] | Darmois, J. G., Les èquations de la gravitation einsteinienne, Memorial des Sciences Mathematiques, Gauthier-Villars, Paris., 25, 1, (1927) · JFM 53.0816.03 |
| [43] | Barrabes, C.; Bressange, G. F., Singular Hypersurfaces in Scalar-Tensor Theories of Gravity, Class. Quantum Gravity, 14, 805-824, (1997) · Zbl 0872.53067 |
| [44] | Deruelle, N.; Sasaki, M.; Sendouda, Y., Junction Conditions in f(R) Theories of Gravity, Prog. Theor. Phys., 119, 237-251, (2008) · Zbl 1152.83019 |
| [45] | Senovilla, J. M.M., Junction conditions for F(R) gravity and their consequences, Phys. Rev. D, 88, 1-11, (2013), 064015 |
| [46] | Clifton, T., Spherically symmetric solutions to fourth-order theories of gravity, Class. Quantum Gravity, 23, 7445-7453, (2006) · Zbl 1107.83047 |
| [47] | Clifton, T.; Dunsby, P.; Goswami, R.; Nzioki, A. M., On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies with f(R) dark energy, Phys. Rev. D, 87, 1-12, (2013), 063517 |
| [48] | Ganguly, A.; Gannouji, R.; Goswami, R.; Ray, S., Neutron stars in the Starobinsky model, Phys. Rev. D, 89, 1-11, (2014), 064019 |
| [49] | Goswami, R.; Nzioki, A. M.; Maharaj, S. D.; Ghosh, S. G., Collapsing spherical stars in f(R) gravity, Phys. Rev. D, 90, 1-10, (2014), 084011 |
| [50] | Lemaitre, G., L’Univers en expansion, Ann. Soc. Sci. Bruxelles A, 53, 51, (1933) · Zbl 0007.33104 |
| [51] | Tolman, R. C., Effect of Inhomogeneity on Cosmological Models, Proc. Natl. Acad. Sci. USA, 20, 3, 169-176, (1934) · JFM 60.0809.02 |
| [52] | Bondi, H., Spherically symmetrical models in general relativity, Mon. Not. R. Astron. Soc., 107, 410-425, (1947) · Zbl 0031.23804 |
| [53] | Chakrabarti, S.; Banerjee, N., Spherically symmetric collapse of a perfect fluid in f(R) gravity, Gen. Relativ. Gravit, 48, 1-9, (2016), 57 · Zbl 1381.83086 |
| [54] | Chakrabarti, S.; Banerjee, N., Gravitational collapse in f(R) gravity for a spherically symmetric spacetime admitting a homothetic Killing vector, Eur. Phys. J. Plus, 131, 1-8, (2016), 144 |
| [55] | Chakrabarti, S.; Goswami, R.; Maharaj, S. D.; Banerjee, N., Conformally flat collapsing stars in f(R) gravity, Gen. Relativ. Grav., 50, 1-23, (2018), 148 · Zbl 1402.83074 |
| [56] | Som, M. M.; Santos, N. O., Expanding viscous fluid with heat flow, Phys. Lett. A, 87, 89-90, (1981) |
| [57] | Maiti, S. R., Fluid with heat flux in a conformally flat space-time, Phys. Rev. D, 25, 2518-2520, (1982) |
| [58] | Modak, B., Cosmological solution with an energy flux, J. Astrophys. Astron., 5, 317-322, (1984) |
| [59] | Banerjee, A.; Dutta Choudhury, S. B.; Bhui, B. K., Conformally flat solution with heat flux, Phy. Rev. D, 40, 670-672, (1989) |
| [60] | Sch¨afer, D.; Goenner, H. F., The Gravitational Field of a Radiating and Contracting Spherically-Symmetric Body with Heat Flow, Gen. Relativ. Grav., 32, 2119-2130, (2000) · Zbl 0959.83034 |
| [61] | Ivanov, B. V., Collapsing shear-free perfect fluid spheres with heat flow, Gen. Relativ. Grav., 44, 1835-1855, (2012) · Zbl 1246.83154 |
| [62] | Herrera, L.; Le Denmat, G.; Santos, N. O.; Wang, A., Shear-free radiating collapse and conformal flatness, Int. J. Mod. Phys. D, 13, 583-592, (2004) · Zbl 1085.83507 |
| [63] | Chakrabarti, S.; Banerjee, N., Scalar field collapse in a conformally flat spacetime, Eur. Phys. J. C, 77, 1-9, (2017), 166 |
| [64] | Banerjee, N.; Chakrabarti, S., Self-similar scalar field collapse, Phys. Rev. D, 95, 1-13, (2017), 024015 |
| [65] | Herrera, L.; Santos, N. O., Local anisotropy in self-gravitating systems, Phys. Rep., 286, 53-130, (1997) |
| [66] | Herrera, L.; Di Prisco, A.; Martin, J.; Ospino, J.; Santos, N. O.; Troconis, O., Spherically symmetric dissipative anisotropic fluids: A general study, Phys. Rev. D, 69, 1-12, (2004), 084026 |
| [67] | Herrera, L.; Ponce de Léon, J., Anisotropic spheres admitting a one-parameter group of conformal motions, J, Math. Phys., 26, 8, 2018-2023, (1985) |
| [68] | Sharif, M.; Bhatti, M. Z., Structure scalars for charged cylindrically symmetric relativistic fluids, Gen. Relativ. Grav., 44, 2811-2823, (2012), Gravitational binding energy in charged cylindrical symmetry, Can. J. Phys. 90 (12) (2012) 1233-1236 · Zbl 1253.83012 |
| [69] | Santos, N. O., Non-adiabatic radiating collapse, Mon. Not. R. Astron. Soc, 216, 403-410, (1985) |
| [70] | Chan, R., Radiating gravitational collapse with shear viscosity, Mon. Not. R. Astron. Soc., 316, 588-604, (2000) |
| [71] | Kolassis, C. A.; Santos, N. O.; Tsoubelis, D., Energy conditions for an imperfect fluid, Class. Quantum Gravity, 5, 1329-1338, (1988) · Zbl 0657.76095 |
| [72] | Pimentel, O. M.; Lora-Clavijo, F. D.; Gonz´alez, G. A., The energy-momentum tensor for a dissipative fluid in general relativity, Gen. Relativ. Gravit., 48, 1-17, (2016), 124 · Zbl 1380.83027 |
| [73] | Paul, B. C.; Debnath, P. S.; Ghose, S., Accelerating universe in modified theories of gravity, Phys. Rev. D, 79, 1-9, (2009), 083534 |
| [74] | Nojiri, S.; Odintsov, S. D., Modified gravity with negative and positive powers of curvature: Unification of inflation and cosmic acceleration, Phys. Rev. D, 68, 1-10, (2003), 123512 |
| [75] | Nojiri, S.; Odintsov, S. D., Modified Gravity with ln R Terms and Cosmic Acceleration, Gen. Rel. Grav., 36, 1765-1780, (2004) · Zbl 1066.83017 |
| [76] | Clifton, T.; Barrow, J. D., The power of general relativity, Phys. Rev. D, 72, 1-21, (2005), 103005 |
| [77] | M. Visser, C. Barcelo, Energy Conditions and their Cosmological Implications COSMO. 99 (2000) 98-112. |
| [78] | Barcelo, C.; Visser, M., Traversable wormholes from massless conformally coupled scalar fields, Phys. Lett. B, 466, 127-134, (1999) · Zbl 0971.83046 |
| [79] | Flanagan, E.; Wald, R., Does back reaction enforce the averaged null energy condition in semiclassical gravity?, Phys. Rev. D, 54, 6233-6283, (1996) |
| [80] | Chakrabarti, S., Collapsing spherical star in Scalar-Einstein-Gauss-Bonnet gravity with a quadratic coupling, Eur. Phys. J. C, 78, 1-13, (2018), 296 |
| [81] | Banerjee, N.; Paul, T., Scalar field collapse in Gauss-Bonnet gravity, Eur. Phys. J. C, 78, 1-6, (2018), 130 |
| [82] | Hamid, A. I.M.; Goswami, R.; Maharaj, S. D., Cosmic censorship conjecture revisited: covariantly, Class. Quantum Gravity, 31, 1-19, (2014), 135010 · Zbl 1295.83047 |
| [83] | Sharif, M.; Abbas, G., Effects of Electromagnetic Field on Gravitational Collapse, Mod. Phys. Lett. A, 24, 2551-2563, (2009) · Zbl 1179.83062 |
| [84] | Zhang, C-Y.; Tang, Z-Y.; Wang, B., Gravitational collapse of massless scalar field in f(R) gravity, Phys. Rev. D, 94, 1-11, (2016), 104013 |
| [85] | Guo, J-Q.; Frolov, A. V., Cosmological dynamics in f(R) gravity, Phys. Rev. D, 88, 1-16, (2013), 124036 |
| [86] | Ziaie, A. H.; Atazadeh, K.; Rasouli, S. M.M., Naked singularity formation in f(R) gravity, Gen Relativ Gravit, 43, 2943-2963, (2011) · Zbl 1228.83087 |
| [87] | Capozziello, S.; De Laurentis, M.; Nojiri, S.; Odintsov, S. D., Classifying and avoiding singularities in the alternative gravity dark energy models, Phys. Rev. D, 79, 1-16, (2009), 124007 |
| [88] | Nazar, H.; Abbas, G., Gravitational collapse in f(R) theories of gravity with non-minimal coupling, Mod. Phys. Lett. A, 34, 1-14, (2019), 1950025 · Zbl 1407.83010 |
| [89] | Sharif, M.; Yousaf, Z., Charged Adiabatic LTB Gravitational Collapse in f(R) Gravity, Int. J. Theor. Phys., 55, 470-480, (2016) · Zbl 1337.83081 |
| [90] | Sharif, M.; Kausar, H. R., Gravitational Perfect Fluid Collapse in f(R) Gravity, Astrophys Space Sci, 331, 281-288, (2011) · Zbl 1209.83034 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
