Abstract
In this present article, we have proposed gravastar under Finslerian spacetime geometry, which can be claimed as an alternative to Finslerian black hole. This study can be considered as a sequel of our previous works based on the Finslerian geometry where we have constructed some phenomenological models for compact stars and wormholes. The concept of gravastar was first proposed by Mazur and Mottola (2001. arXiv:gr-qc/0109035; Proc Natl Acad Sci USA 101:9545, 2004) which consist of three regions in its configuration namely (I) the interior core, (II) the intermediate thin shell, and (III) the vacuum exterior. These three regions can be described by three different equation of state. Here we solve gravastar under the framework of Finsler geometry and obtain a set of exact and physically acceptable solutions for three different regions. We have also studied various physical parameters which are fulfilled by the physical requirement for validity of the present study on gravastar within the Finslerian spacetime geometry.
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References
P. Mazur, E. Mottola, arXiv:gr-qc/0109035. Report number: LA-UR-01-5067 (2001)
P. Mazur, E. Mottola, Proc. Natl. Acad. Sci. USA 101, 9545 (2004)
M. Visser et al., Class. Quantum Gravity 21, 1135 (2004)
A.A. Usmani, P.P. Ghosh, U. Mukhopadhyay, P.C. Ray, S. Ray, Mon. Not. R. Astron. Soc. 386, L92 (2008)
F. Rahaman, R. Maulick, A.K. Yadav, S. Ray, R. Sharma, Gen. Relat. Gravity 44, 107 (2012)
A.A. Usmani, F. Rahaman, S. Ray, K.K. Nandi, P.K.F. Kuhfittig, SkA Rakib, Z. Hasan, Phys. Lett. B 701, 388 (2011)
F. Rahaman, S. Chakraborty, S. Ray, A.A. Usmani, S. Islam, Int. J. Theor. Phys. 54, 50 (2015)
F. Rahaman et al., Phys. Lett. B 717, 1 (2012)
P. Bhar, Astrophys. Space Sci. 354, 2109 (2014)
S. Ghosh, F. Rahaman, B.K. Guha, S. Ray, Phys. Lett. B 767, 380 (2017)
S. Ghosh, S. Ray, F. Rahaman, B.K. Guha, Ann. Phys. 394, 230 (2018)
A. Das, S. Ghosh, B.K. Guha, S. Das, F. Rahaman, S. Ray, Phys. Rev. D 95, 124011 (2017)
P. Bhar. arXiv:1702.02467
A. Das, S. Ghosh, B.K. Guha, S. Das, F. Rahaman, S. Ray, communicated
E. Cartan, Les Espaces de Finsler (Herman, Paris, 1935)
J.I. Horváth, Phys. Rev. 80, 2001 (1950)
D. Bao, S.S. Chern, Z. Shen, An Introduction to Riemann–Finsler Geometry, Graduate Texts in Mathematics (Springer, New York, 2000)
S. Vacaru, Int. J. Mod. Phys. D 21, 1250072 (2012). arXiv:1004.3007
S. Vacaru, Nucl. Phys. B 434, 590–656 (1997). arXiv:hep-th/9611034
S. Vacaru, J. Math. Phys. 37, 508–523 (1996)
X. Li, Z. Chang, Phys. Rev. D 90, 064049 (2014)
S.I. Vacaru, Class. Quantum Gravity 27, 105003 (2010)
F. Rahaman, N. Paul, S.S. De, S. Ray, Md A. Kayum Jafry, Eur. Phys. J. C 75, 564 (2015)
F. Rahaman, N. Paul, A. Banerjee, S.S. De, S. Ray, A.A. Usmani, Eur. Phys. J. C 76, 246 (2016)
G. Darmois, Memorial des sciences mathematiques XXV, Fasticule XXV ch V (Gauthier-Villars, Paris, 1927)
W. Israel, Nuo. Cim. B 44, 1 (1966)
W. Israel, Nuo. Cim. B 48, 463 (1966)
C. Lanczos, Ann. Phys. 74, 518 (1924)
N. Sen, Ann. Phys. 378, 365 (1924)
G.P. Perry, R.B. Mann, Gen. Relativ. Gravity 24, 305 (1992)
P. Musgrave, K. Lake, Class. Quantum Gravity 13, 1885 (1996)
T. Kubo, N. Sakai, Phys. Rev. D 93, 084051 (2016)
P. Pani, E. Berti, V. Cardoso, Y. Chen, R. Norte, Phys. Rev. D 80, 124047 (2009)
P. Pani, E. Berti, V. Cardoso, Y. Chen, R. Norte, J. Phys. Conf. Ser. 222, 012032 (2010)
P. Pani, E. Berti, V. Cardoso, Y. Chen, R. Norte, Phys. Rev. D 81, 084011 (2010)
B.P. Abbott et al., (LIGO/Virgo Scientific Collaboration), Phys. Rev. Lett. 116, 061102 (2016)
V. Cardoso, E. Franzin, P. Pani, Phys. Rev. Lett. 116, 171101 (2016)
V. Cardoso, E. Franzin, P. Pani, Phys. Rev. Lett. 117, 089902 (E) (2016)
C. Chirenti, L. Rezzolla, Phys. Rev. D 94, 084016 (2016)
K. Bamba, S. Capozziello, M.D. Laurentis, S. Nojiri, D. Sáez-Gómez, Phys. Lett. B 727, 194 (2013)
J. Aron, New Scientist, issue 3072, 4 May (2016)
Acknowledgements
FR would like to thank the authorities of the Inter-University Centre for Astronomy and Astrophysics, Pune, India for providing research facilities. FR and NP are also grateful to DST-SERB (Grant No.: EMR/2016/000193), Govt. of India and Non-Net fellowship, Govt. of West Bengal for financial support, respectively.
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Banerjee, S., Ghosh, S., Paul, N. et al. Study of gravastars in Finslerian geometry. Eur. Phys. J. Plus 135, 185 (2020). https://doi.org/10.1140/epjp/s13360-020-00230-0
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DOI: https://doi.org/10.1140/epjp/s13360-020-00230-0