Journal of Holography Applications in Physics
Geodesic motion in the spacetime of a (2 + 1) D black hole conformally coupled to a massless scalar
Document Type : Regular article
Author
Yasouj University, Iran
Abstract
In this paper, we consider a (2+1) D black hole conformally coupled to a massless scalar. Then the geodesic motion of test particles and light rays in the vicinity of the spacetime of this black hole is studied. Moreover, the geodesic equations are solved analytically according to Weierstrass elliptic and derivatives of Kleinian sigma hyperelliptic functions. Also, the possible orbits are discussed and classified according to the particle's energy and angular momentum.
Keywords
Main Subjects
Article PDF
[1] M. Banados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space- time, Phys. Rev. Lett. 69, 1849-1851 (1992) [arXiv:hep-th/9204099 [hep-th]].
[2] M. Banados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2+1) black hole, Phys. Rev. D 48, 1506-1525 (1993) [erratum: Phys. Rev. D 88, 069902 (2013)].
[3] M. Cataldo, N. Cruz, S. del Campo and A. Garcia, (2+1)-dimensional black hole with Coulomb - like field, Phys. Lett. B 484, 154 (2000) [arXiv:hep-th/0008138 [hep-th]].
[4] C. Martinez and J. Zanelli, Conformally dressed black hole in (2+1)-dimensions, Phys. Rev. D 54, 3830 (1996) [grqc/9604021].
[5] M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Black holes and asymptotics of 2+1 gravity coupled to a scalar field, Phys. Rev. D 65, 104007 (2002) [hep-th/0201170].
[6] F. Correa, C. Martinez and R. Troncoso,Scalar solitons and the microscopic entropy of hairy black holes in three dimensions, JHEP 1101, 034 (2011). [arXiv:1010.1259 [hep-th]].
[7] F. Correa, C. Martinez and R. Troncoso, Hairy Black Hole Entropy and the Role of Solitons in Three Dimensions, JHEP 1202, 136 (2012). [arXiv:1112.6198 [hep-th]].
[8] W. Xu and D. C. Zou, (2+1) Dimensional charged black holes with scalar hair in Einstein Power Maxwell Theory, Gen. Rel. Grav. 49, no.6, 73 (2017).
[9] W. Xu and L. Zhao, Charged black hole with a scalar hair in (2+1) dimensions, Phys. Rev. D 87, no.12, 124008 (2013) [arXiv:1305.5446 [gr-qc]].
[10] M. Cataldo and A. Garcia, Regular (2+1)-dimensional black holes within nonlinear electrodynamics, Phys. Rev. D 61, 084003 (2000) [arXiv:hep-th/0004177 [hep-th]].
[11] S. Habib Mazharimousavi, M. Halilsoy and T. Tahamtan, Regular charged black hole construction in 2+1 -dimensions, Phys. Lett. A 376, 893-898 (2012).
[12] Y. He and M. S. Ma, (2 + 1)-dimensional regular black holes with nonlinear electrodynamics sources, Phys. Lett. B 774, 229-234 (2017) [arXiv:1709.09473 [gr-qc]].
[13] S Chandrasekhar (Oxford: Clarendon press) (1985).
[14] E Hackmann V Kagramanova J Kunz and C Lammerzahl, Physical Review D 78 124018 (2008) Erratum [Physical Review D 79 029901 (2009)].
[15] E Hackmann and C Lammerzahl, Physical Review Letters 100 171101 (2008).
[16] E Hackmann C Lammerzahl V Kagramanova and J Kunz Physical Review D 81 044020 (2010).
[17] S Soroushfar R Saffari J Kunz and C Lammerzahl Physical Review D 92 044010 (2015).
[18] B Hoseini R Saffari S Soroushfar J Kunz and S Grunau Physical Review D 94 044021 (2016).
[19] V Z Enolski E Hackmann V Kagramanova J Kunz and C Lammerzahl Journal of Geometry and Physics 61 899 (2011).
[20] V Kagramanova and S Reimers Physical Review D 86 084029 (2012). V Diemer J Kunz
C Lammerzahl and S Reimers Physical Review D 89124026 (2014). [21] S Soroushfar R Saffari S Kazempour S Grunau and J Kunz Physical Review D 94 024052 (2016).
[22] S. Soroushfar, R. Saffari, and A. Jafari, Phys. Rev. D 93, 104037 (2016).
[23] S. Soroushfar, M. Afrooz, Analytical solutions of the geodesic equation in the spacetime of a black hole surrounded by perfect fluid in Rastall theory. Indian J Phys 96, 593-607 (2022).
[24] C. Martinez and J. Zanelli, Phys. Rev. D 54, 3830 (1996).
[25] H.K. Sudhanshu, S. Upadhyay, D.V. Singh, et al. Corrected Thermodynamics of (2+1)D Black Hole Conformally Coupled to a Massless Scalar. Int J Theor Phys 61, 248 (2022).
[2] M. Banados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2+1) black hole, Phys. Rev. D 48, 1506-1525 (1993) [erratum: Phys. Rev. D 88, 069902 (2013)].
[3] M. Cataldo, N. Cruz, S. del Campo and A. Garcia, (2+1)-dimensional black hole with Coulomb - like field, Phys. Lett. B 484, 154 (2000) [arXiv:hep-th/0008138 [hep-th]].
[4] C. Martinez and J. Zanelli, Conformally dressed black hole in (2+1)-dimensions, Phys. Rev. D 54, 3830 (1996) [grqc/9604021].
[5] M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Black holes and asymptotics of 2+1 gravity coupled to a scalar field, Phys. Rev. D 65, 104007 (2002) [hep-th/0201170].
[6] F. Correa, C. Martinez and R. Troncoso,Scalar solitons and the microscopic entropy of hairy black holes in three dimensions, JHEP 1101, 034 (2011). [arXiv:1010.1259 [hep-th]].
[7] F. Correa, C. Martinez and R. Troncoso, Hairy Black Hole Entropy and the Role of Solitons in Three Dimensions, JHEP 1202, 136 (2012). [arXiv:1112.6198 [hep-th]].
[8] W. Xu and D. C. Zou, (2+1) Dimensional charged black holes with scalar hair in Einstein Power Maxwell Theory, Gen. Rel. Grav. 49, no.6, 73 (2017).
[9] W. Xu and L. Zhao, Charged black hole with a scalar hair in (2+1) dimensions, Phys. Rev. D 87, no.12, 124008 (2013) [arXiv:1305.5446 [gr-qc]].
[10] M. Cataldo and A. Garcia, Regular (2+1)-dimensional black holes within nonlinear electrodynamics, Phys. Rev. D 61, 084003 (2000) [arXiv:hep-th/0004177 [hep-th]].
[11] S. Habib Mazharimousavi, M. Halilsoy and T. Tahamtan, Regular charged black hole construction in 2+1 -dimensions, Phys. Lett. A 376, 893-898 (2012).
[12] Y. He and M. S. Ma, (2 + 1)-dimensional regular black holes with nonlinear electrodynamics sources, Phys. Lett. B 774, 229-234 (2017) [arXiv:1709.09473 [gr-qc]].
[13] S Chandrasekhar (Oxford: Clarendon press) (1985).
[14] E Hackmann V Kagramanova J Kunz and C Lammerzahl, Physical Review D 78 124018 (2008) Erratum [Physical Review D 79 029901 (2009)].
[15] E Hackmann and C Lammerzahl, Physical Review Letters 100 171101 (2008).
[16] E Hackmann C Lammerzahl V Kagramanova and J Kunz Physical Review D 81 044020 (2010).
[17] S Soroushfar R Saffari J Kunz and C Lammerzahl Physical Review D 92 044010 (2015).
[18] B Hoseini R Saffari S Soroushfar J Kunz and S Grunau Physical Review D 94 044021 (2016).
[19] V Z Enolski E Hackmann V Kagramanova J Kunz and C Lammerzahl Journal of Geometry and Physics 61 899 (2011).
[20] V Kagramanova and S Reimers Physical Review D 86 084029 (2012). V Diemer J Kunz
C Lammerzahl and S Reimers Physical Review D 89124026 (2014). [21] S Soroushfar R Saffari S Kazempour S Grunau and J Kunz Physical Review D 94 024052 (2016).
[22] S. Soroushfar, R. Saffari, and A. Jafari, Phys. Rev. D 93, 104037 (2016).
[23] S. Soroushfar, M. Afrooz, Analytical solutions of the geodesic equation in the spacetime of a black hole surrounded by perfect fluid in Rastall theory. Indian J Phys 96, 593-607 (2022).
[24] C. Martinez and J. Zanelli, Phys. Rev. D 54, 3830 (1996).
[25] H.K. Sudhanshu, S. Upadhyay, D.V. Singh, et al. Corrected Thermodynamics of (2+1)D Black Hole Conformally Coupled to a Massless Scalar. Int J Theor Phys 61, 248 (2022).
)
Volume 3, Issue 1
March 2023Pages 49-56
- Receive Date: 25 January 2023
- Revise Date: 25 February 2023
- Accept Date: 10 March 2023