Abstract.
The idea of this work is to exhibit the unstable regions of a self-gravitating celestial object which collapses adiabatically with a non-vanishing expansion scalar. We adopted the generalized teleparallel gravity for a plane-symmetric self-gravitating object and matter distribution as dissipative and anisotropic. We analyzed the instability regions of the stellar model by considering a particular model, i.e., \(\beta T + \gamma T^{n}\). We established the basic dynamical equations together with junction conditions and equation of state proposed by Harrison et al. The linear perturbation strategy is applied to the metric, matter and f (T) function up to first order. The equations of motion are developed under this perturbative framework to construct collapse equation. We demonstrate the unstable phases at weak field limit and post-Newtonian epochs and deduce a vital role of adiabatic index to explain the stability/instability issues for planar model in f (T) gravity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.W. Maluf, Universe 70, 04385 (2016)
S. Nojiri, S.D. Odintsov, eConf C 06, 0602061 (2006) Int. J. Geom. Methods Mod. Phys. 4
S. Capozziello, M.D. Laurentis, Phys. Rep. 509, 167 (2011)
E.J. Copeland, M. Sami, S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753 (2006)
Y.F. Cai, E.N. Saridakis, M.R. Setare, J.Q. Xia, Phys. Rep. 1, 493 (2010)
K.S. Stelle, Phys. Rev. D 16, 953 (1977)
T. Biswas, E. Gerwick, T. Koivisto, A. Mazumdar, Phys. Rev. Lett. 108, 031101 (2012)
R. Ferraro, F. Fiorini, Phys. Rev. D 75, 084031 (2007)
C.Q. Geng, C.C. Lee, E.N. Saridakis, Y.P. Wu, Phys. Lett. B 384, 704 (2011)
K. Bamba, C.Q. Geng, C.C. Lee, L.W. Luo, J. Cosmol. Astropart. Phys. 01, 021 (2011)
K. Bamba, R. Myrzakulov, S. Nojiri, S.D. Odintsov, Phys. Rev. D 85, 104036 (2012)
K. Bamba, C.Q. Geng, J. Cosmol. Astropart. Phys. 11, 008 (2011)
S. Bahamonde, C.G. Boehmer, M. Wright, Phys. Rev. D 92, 104042 (2015)
R. Aldrovandi, J.G. Pereira, K.H. Vu, Braz. J. Phys. 34, 1374 (2004)
T. Vargas, Gen. Relativ. Gravit. 36, 1255 (2004)
R. Ferraro, F. Fiorini, Phys. Rev. D 78, 124019 (2008)
M. Jamil, D. Momeni, R. Myrzakulov, Eur. Phys. J. C 72, 2137 (2012)
T. Wang, Phys. Rev. D 84, 024042 (2011)
A. Jawad, S. Rani, Eur. Phys. J. C 75, 548 (2015)
K. Izumi, Y.C. Ong, J. Cosmol. Astropart. Phys. 06, 029 (2013)
B. Li, T.P. Sotiriou, J.D. Barrow, Phys. Rev. D 83, 104017 (2011)
H.I. Acros, T.G. Lucas, J.G. Pereira, Class. Quantum Grav. 27, 145007 (2010)
S. Capozziello, M. Francaviglia, Gen. Relativ. Gravit. 40, 357 (2008)
R. Gosh, A. Pasqua, S. Chattopadhyay, Eur. Phys. J. Plus 128, 12 (2013)
M. Krššák, E.N. Saridakis, Class. Quantum Grav. 33, 115009 (2016)
K. Bamba, S. Nojiri, S.D. Odintsov, Phys. Lett. B 725, 368 (2013)
G.G.L. Nashed, Adv. High Energy Phys. 1, 680457 (2015)
A. Lichnerowicz, Theories Relativistes de le Gravitation et de l’Electromagnétisme, Masson, (1955) chapt. I, III
G. Darmois, Memorial des Sciences Mathematiques (Gautheir-Villars, Paris, 1927) Fasc. 25
S. O’Brien, J.L. Synge, Jump Conditions at Discontinuities in General Relativity, in Communications of the Dublin Institute for Advanced Studies, A, Vol. 9 (Dublin Institute for Advanced Studies, 1952)
S. Chandrasekhar, Astrophys. J. 140, 417 (1964)
L. Herrera, N.O. Santos, G. Le Denmat, Mon. Not. R. Astron. Soc. 237, 257 (1989)
L. Herrera, N.O. Santos, Astrophys. J. 308, 438 (1995)
R. Chan, Mon Not. R. Astron. Soc. 316, 588 (2000)
M. Sharif, M.Z. Bhatti, J. Cosmol. Astropart. Phys. 11, 014 (2013)
M. Sharif, Z. Yousaf, J. Cosmol. Astropart. Phys. 06, 019 (2014)
M. Sharif, Z. Yousaf, Astrophys. Space Sci. 352, 943 (2014) arXiv:1405.1378v3 [gr-qc]
S. Capozziello, M. De Laurentis, I. De Martino, M. Formisano, S.D. Odintsov, Phys. Rev. D 85, 044022 (2012)
M. Sharif, Z. Yousaf, Mon. Not. R. Astron. Soc. 440, 3479 (2014)
M. Sharif, Z. Yousaf, Astrophys. Space Sci. 357, 49 (2015)
M. Sharif, Z. Yousaf, Can. J. Phys. 93, 905 (2015)
M. Sharif, Z. Yousaf, Gen. Relativ. Gravit. 47, 48 (2015)
M.Z. Bhatti, Eur. Phys. J. Plus 131, 428 (2016)
Z. Yousaf, K. Bamba, M.Z. Bhatti, Phys. Rev. D 95, 024024 (2017) arXiv:1701.03067 [gr-qc]
Z. Yousaf, M.Z. Bhatti, A. Rafaqat, Int. J. Mod. Phys. D 26, 1750099 (2017)
M.Z. Bhatti, Z. Yousaf, Int. J. Mod. Phys. D 26, 1750029 (2017)
Z. Yousaf, Eur. Phys. J. Plus 132, 71 (2017)
M. Sharif, M.Z. Bhatti, J. Exp. Theor. Phys. 120, 813 (2015)
M. Sharif, Z. Yousaf, Eur. Phys. J. C 75, 194 (2015) arXiv:1504.04367[gr-qc]
M. Sharif, Z. Yousaf, Eur. Phys. J. C 75, 58 (2015)
M. Sharif, Z. Yousaf, Astrophys. Space Sci. 355, 317 (2015)
P. Wu, H. Yu, Phys. Lett. B 223, 703 (2011)
A. Jawad, S. Rani, Eur. Phys. J. C 75, 173 (2015)
A. Jawad, D. Momeni, S. Rani, R. Myrzakulov, Astrophys. Space Sci. 361, 141 (2016)
P.A. González, J. Saavedra, Y. Vásquez, Astrophys. Space Sci. 357, 143 (2015)
M.Z. Bhatti, Z. Yousaf, Eur. Phys. J. C 76, 219 (2016) arXiv1604.01395 [gr-qc]
Z. Yousaf, M.Z. Bhatti, Mon. Not. R. Astron. Soc. 458, 1785 (2016) arXiv:1612.02325 [physics.gen-ph]
M.Z. Bhatti, Z. Yousaf, Int. J. Mod. Phys. D 26, 1750045 (2017)
Z. Yousaf, K. Bamba, M.Z. Bhatti, Phys. Rev. D 93, 064059 (2016) arXiv1603.03175 [gr-qc]
Z. Yousaf, K. Bamba, M.Z. Bhatti, Phys. Rev. D 93, 124048 (2016) arXiv1606.00147 [gr-qc]
Z. Yousaf, M.Z. Bhatti, U. Farwa, Mon. Not. R. Astron. Soc. 464, 4509 (2017)
Ch.C. Moustakidis, arXiv:1612.01726 [gr-qc]
K. Bamba, M. Jamil, D. Momeni, R. Myrzakulov, Astrophys. Space Sci. 344, 259 (2013)
K. Bamba, S.D. Odintsov, D. Sáez-Gómez, Phys. Rev. D 88, 084042 (2013)
Y.F. Cai, S. Capozziello, M. De Laurentis, E.N. Saridakis, Rep. Prog. Phys. 79, 106901 (2016)
M.Z. Bhatti, Z. Yousaf, S. Hanif, Phys. Dark Universe 16, 34 (2017)
T. Zannias, Phys. Rev. D 41, 3252 (1990)
H. Chao-Guang, Acta Phys. Sin. 4, 617 (1995)
R. Myrzakulov, Eur. Phys. J. C 71, 1752 (2011)
B.K. Harrison, K.S. Thorne, M. Wakano, J.A. Wheeler, Gravitation Theory and Gravitational Collapse (University of Chicago Press, 1965)
L. Herrera, G. Le Denmat, N.O. Santos, Gen. Relativ. Gravit. 44, 1143 (2012)
M. Sharif, M.Z. Bhatti, Astrophys. Space Sci. 355, 389 (2015)
Z. Yousaf, M.Z. Bhatti, Eur. Phys. J. C 76, 267 (2016) arXiv:1604.06271 [physics.gen-ph]
S. Capozziello, M. De Laurentis, I. De Martino, M. Formisano, S.D. Odintsov, Phys. Rev. D 85, 044022 (2012)
A.K. Ahmed, M. Azreg-Ainou, S. Bahamonde, S. Capozziello, M. Jamil, Eur. Phys. J. C 76, 269 (2016)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zaeem-ul-Haq Bhatti, M., Yousaf, Z. & Hanif, S. Gravitational collapse in generalized teleparallel gravity. Eur. Phys. J. Plus 132, 230 (2017). https://doi.org/10.1140/epjp/i2017-11505-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2017-11505-x