Journal of Holography Applications in Physics
How are the degrees of freedom responsible for entropy in BTZ spacetime?
Document Type : Letter
Authors
1 Department of Physics, Institute of Applied Sciences and Humanities, GLA University Mathura, India. Centre for Theoretical Physics.
2 Department of Physics Daulat Ram College University of Delhi
Abstract
The entanglement entropy approach to study the dependence of entropy upon the location of degrees
of freedom (dof ) (near/far) from the horizon is discussed in this article. We try to understand the
physical deviation of the area law for the excited states by incorporating the logarithmic and power
law corrections. We show that the dof near the horizon gives contribution to the total entropy of
the system in the ground state and away from the event horizon gives contribution to the excited
state.
Keywords
Main Subjects
Article PDF
[1] J.D. Bekenstein, ”Black Holes and Entropy”, Phy. Rev. D 7, 2333 (1973).
[2] J.D. Bekenstein, ”Black holes and the second law”, Lett. al Nuovo Ciemnto 4, 15 (1972).
[3] J.D. Bekenstein, ”Generalized second law of thermodynamics in black-hole physics”, Phy. Rev. D 9, 3292 (1974).
[4] J.D. Bekenstein, ”Statistical black-hole thermodynamics”, Phy. Rev. D 12, 3077 (1975).
[5] S.W. Hawking, ”Black holes and thermodynamics”, Phy. Rev. D 13, 191 (1976).
[6] S. Carlip, ”The (2+1)-Dimensional Black Hole”, Class. Quantum Gravity 12, 2853 (1995).
[7] M. R. Setare and H. Adami, ”Entropy formula of black holes in minimal massive gravity and its application for BTZ black holes”, Phys. Rev. D 91 (2015) no.10, 104039.
[8] M. R. Setare and V. Kamali, ”Correspondence between the contracted BTZ solution of cosmological topological massive gravity and two-dimensional Galilean conformal algebra”, Class. Quant. Grav. 28, 215004 (2011).
[9] F. Darabi, M. Jamil and M. R. Setare, ”Self-gravitational corrections to the Cardy-Verlinde formula of charged BTZ black hole” Mod. Phys. Lett. A 26, 1047 (2011).
[10] M. R. Setare and M. Jamil, ”The Cardy-Verlinde Formula and Entropy of the Charged Rotating BTZ black Hole” Phys. Lett. B 681, 469-471 (2009).
[11] M. Cadoni and M. R. Setare, ”Near-horizon limit of the charged BTZ black hole and AdS(2) quantum gravity”, JHEP 07, 131 (2008).
[12] M. Cadoni, M. Melis and M. R. Setare, ”Microscopic entropy of the charged BTZ black hole”, Class. Quant. Grav. 25, 195022 (2008).
[13] M. R. Setare, ”Gauge and gravitational anomalies and Hawking radiation of rotating BTZ black holes”, Eur. Phys. J. C 49, 865-868 (2007).
[14] M. R. Setare, ”Nonrotating BTZ black hole area spectrum from quasinormal modes”, Class. Quant. Grav. 21, 1453-1458 (2004).
[15] S. Upadhyay, N,-ul-islam, P. A. Ganai, ”A modified thermodynamics of rotating and charged BTZ black hole”, JHAP 2, 25 (2022).
[16] N.-ul Islam, P. A. Ganai, S. Upadhyay, ”Thermal fluctuations to thermodynamics of non-rotating BTZ black hole”, Prog. Theor. Exp. Phys. 103B06 (2019).
[17] S. H. Hendi, S. Panahiyan, S. Upadhyay, B. E. Panah, ”Charged BTZ black holes in the context of massive gravity’s rainbow”, Phys. Rev. D 95, 084036 (2017).
[18] L. Bombelli, R. K. Koul, J. Lee and R. D. Sorkin, ”Quantum Source of entropy for Black Hole”, Phy. Rev. D 34, 373 (1986).
[19] M. Srednicki, “Entropy and Area” Phy. Rev. Lett.71, 666 (1993).
[20] S. Das and S. Shankaranarayanan, ”How robust is the entanglement entropy: Area relation?”, Phys. Rev. D 73, (2006).
[21] S. Das, S. Shankaranarayanan, S. Sur, ”Black hole entropy from entanglement: A review”, Horizons in World Physics 268 (2009) [arXiv:0806.0402 [gr-qc]].
[22] S. Das and S Shankarnarayanan, ”Where are the black hole entropy degree of freedom?”, Classical and Quantum Gravity 24 5299-5306 (2007).
[23] L. Susskind, Entanglement and Chaos in De Sitter Space Holography: An SYK Exam- ple. Journal of Holography Applications in Physics 1, 1-22 (2021).
[24] B. Kay, ”Entanglement entropy and algebraic holography”, Journal of Holography Applications in Physics 1, 23-36 (2021).
[25] F.dos Santos, ”Entanglement entropy in Horndeski gravity”, Journal of Holography Applications in Physics 3, 1-14 (2022).
[26] H. Casini and M. Huerta, ”Entanglement entropy in free quantum field theory”, J. Phys. A 42, 504007 (2009).
[27] S. N. Solodukhin, ”Entanglement entropy of black holes”, Living Rev. Rel. 14, (2011)8.
[28] M. Huerta, ”Numerical Determination of the Entanglement Entropy for Free Fields in the Cylinder”, Phys. Lett. B 710, 691 (2012).
[29] D. V. Singh and S. Siwach, ”Thermodynamics of BTZ Black Hole and Entanglement Entropy”, Journal of phys. Conf. Series 481, 012014 (2014).
[30] D. V. Singh and S. Sachan, ”Logarithmic Corrections to the Entropy of Scalar Field in BTZ Black Hole Space-time”, Int. Journal of Mod. Phys. D 26, 1750038 (2017).
[31] M. Cadoni, ”Entanglement entropy of two-dimensional Anti-de Sitter black holes”, Phys. Lett. B 653, 434 (2007).
[32] M. Cadoni and M. Melis, “Holographic entanglement entropy of the BTZ black hole,” Found. Phys. 40, 638 (2010).
[33] M. Cadoni and M. Melis, ”Entanglement Entropy of AdS Black Holes”, Entropy 12, 2244-2267 (2010).
[34] A. Chatterjee and P. Majumdar, ”Black hole entropy: Quantum versus thermal fluctuations”, [arXiv: gr-qc/0303030].
[35] B. Pourhassan, H. Aounallah, M.Faizal, S. Upadhyay, S. Soroushfar, Y. O. Aitenov, S. S. Wani, ”Quantum thermodynamics of an M2-M5 brane system”, JHEP 05, 030 (2022).
[36] B. Pourhassan, S. Upadhyay, ”Perturbed thermodynamics of charged black hole solution in Rastall theory”, Eur. Phys. J. Plus 136, 311 (2021).
[37] S. Upadhyay, B. Pourhassan, ”Logarithmic corrected Van der Waals black holes in higher dimensional AdS space”, Prog. Theor. Exp. Phys. 013B03 (2019).
[38] S. Upadhyay, ”Leading-order corrections to charged rotating AdS black holes thermodynamics”, Gen. Rel. Grav. 50, 128 (2018).
[39] S. Upadhyay, ”Quantum corrections to thermodynamics of quasitopological black holes”, Phys. Lett. B 775, 130 (2017).
[40] S. Upadhyay, B. Pourhassan, H. Farahani, ”P-V criticality of first-order entropy corrected AdS black holes in massive gravity”, Phys. Rev. D 95, 106014 (2017).
[41] B. Pourhassan, M. Faizal, S. Upadhyay, L. A. Asfar, ”Thermal Fluctuations in a Hyperscaling Violation Background”, Eur. Phys. J. C 77, 555 (2017).
[42] A. Strominger, C. Vafa, ”Microscopic Origin of the Bekenstein-Hawking Entropy” Phys. Lett. B 379, 99, (1996).
[43] A. Ashtekar, J. Baez, A. Corichi and K. Krasnov, ”Quantum geometry and black hole entropy”, Phys. Rev. Lett. 80, 904 (1998).
[44] A. Dasgupta, ”Semi-classical quantisation of space-times with apparent horizons”, Class. Quant. Grav. 23, 635 (2006).
[45] S. Das, S. Shankaranarayanan and S. Sur, ”Power-law corrections to entanglement entropy of black holes” Phys. Rev. D 77, 064013 (2008).
[46] D V Singh, ”Power law corrections to BTZ Black hole Entropy” Int. J. Mod. Phys. D 24, 1550001 (2015).
[47] D. V. Singh and S. Siwach ”Scalar Field in BTZ Black Hole Space-time and Entanglement Entropy”, Class. Quantum Grav. 30, 235034 (2013).
[48] D. V. Singh and S. Siwach, ”Fermion Field in BTZ Black Hole Space-time and Entanglement Entropy”, Adv. High Energy Phys. 2015, 528762 (2015).
[49] M Banados, C Teitelboim and J Zanelli, “The Black Hole in Three Dimensional Space-time” Phy. Rev. Lett. 69, 1849 (1992).
[50] R.B.Mann and S.N.Solodukhin, ”Quantum scalar field on three-dimensional (BTZ) black hole instanton: Heat kernel, effective action and thermodynamics”, Phys. Rev. D 55, 3622 (1997).
[51] D. V. Singh and N. K. Singh, ”Anti-Evaporation of Bardeen de-Sitter Black Holes”, Annals Phys. 383, 600-609 (2017).
[52] D. V. Singh, M. S. Ali and S. G. Ghosh, ”Noncommutative geometry inspired rotating black string”, Int. J. Mod. Phys. D 27, 1850108 (2018).
[53] D. V. Singh and S. Siwach, ”On Thermodynamics and Statistical Entropy of Bardeen Black Hole”, [arXiv:1909.11529 [hep-th]].
[54] D. V. Singh, S. Upadhyay and M. S. Ali, ”Rotating Lee–Wick black hole and thermodynamics” Int. J. Mod. Phys. A 37, 2250049 (2022).
[55] D. V. Singh, S. G. Ghosh and S. D. Maharaj, ”Exact nonsingular black holes and thermodynamics”, Nucl. Phys. B 981, 115854 (2022).
[56] D. V. Singh and S. Siwach, ”Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4D Einstein-Gauss-Bonnet Gravity”, Phys. Lett. B 808, 135658 (2020).
[2] J.D. Bekenstein, ”Black holes and the second law”, Lett. al Nuovo Ciemnto 4, 15 (1972).
[3] J.D. Bekenstein, ”Generalized second law of thermodynamics in black-hole physics”, Phy. Rev. D 9, 3292 (1974).
[4] J.D. Bekenstein, ”Statistical black-hole thermodynamics”, Phy. Rev. D 12, 3077 (1975).
[5] S.W. Hawking, ”Black holes and thermodynamics”, Phy. Rev. D 13, 191 (1976).
[6] S. Carlip, ”The (2+1)-Dimensional Black Hole”, Class. Quantum Gravity 12, 2853 (1995).
[7] M. R. Setare and H. Adami, ”Entropy formula of black holes in minimal massive gravity and its application for BTZ black holes”, Phys. Rev. D 91 (2015) no.10, 104039.
[8] M. R. Setare and V. Kamali, ”Correspondence between the contracted BTZ solution of cosmological topological massive gravity and two-dimensional Galilean conformal algebra”, Class. Quant. Grav. 28, 215004 (2011).
[9] F. Darabi, M. Jamil and M. R. Setare, ”Self-gravitational corrections to the Cardy-Verlinde formula of charged BTZ black hole” Mod. Phys. Lett. A 26, 1047 (2011).
[10] M. R. Setare and M. Jamil, ”The Cardy-Verlinde Formula and Entropy of the Charged Rotating BTZ black Hole” Phys. Lett. B 681, 469-471 (2009).
[11] M. Cadoni and M. R. Setare, ”Near-horizon limit of the charged BTZ black hole and AdS(2) quantum gravity”, JHEP 07, 131 (2008).
[12] M. Cadoni, M. Melis and M. R. Setare, ”Microscopic entropy of the charged BTZ black hole”, Class. Quant. Grav. 25, 195022 (2008).
[13] M. R. Setare, ”Gauge and gravitational anomalies and Hawking radiation of rotating BTZ black holes”, Eur. Phys. J. C 49, 865-868 (2007).
[14] M. R. Setare, ”Nonrotating BTZ black hole area spectrum from quasinormal modes”, Class. Quant. Grav. 21, 1453-1458 (2004).
[15] S. Upadhyay, N,-ul-islam, P. A. Ganai, ”A modified thermodynamics of rotating and charged BTZ black hole”, JHAP 2, 25 (2022).
[16] N.-ul Islam, P. A. Ganai, S. Upadhyay, ”Thermal fluctuations to thermodynamics of non-rotating BTZ black hole”, Prog. Theor. Exp. Phys. 103B06 (2019).
[17] S. H. Hendi, S. Panahiyan, S. Upadhyay, B. E. Panah, ”Charged BTZ black holes in the context of massive gravity’s rainbow”, Phys. Rev. D 95, 084036 (2017).
[18] L. Bombelli, R. K. Koul, J. Lee and R. D. Sorkin, ”Quantum Source of entropy for Black Hole”, Phy. Rev. D 34, 373 (1986).
[19] M. Srednicki, “Entropy and Area” Phy. Rev. Lett.71, 666 (1993).
[20] S. Das and S. Shankaranarayanan, ”How robust is the entanglement entropy: Area relation?”, Phys. Rev. D 73, (2006).
[21] S. Das, S. Shankaranarayanan, S. Sur, ”Black hole entropy from entanglement: A review”, Horizons in World Physics 268 (2009) [arXiv:0806.0402 [gr-qc]].
[22] S. Das and S Shankarnarayanan, ”Where are the black hole entropy degree of freedom?”, Classical and Quantum Gravity 24 5299-5306 (2007).
[23] L. Susskind, Entanglement and Chaos in De Sitter Space Holography: An SYK Exam- ple. Journal of Holography Applications in Physics 1, 1-22 (2021).
[24] B. Kay, ”Entanglement entropy and algebraic holography”, Journal of Holography Applications in Physics 1, 23-36 (2021).
[25] F.dos Santos, ”Entanglement entropy in Horndeski gravity”, Journal of Holography Applications in Physics 3, 1-14 (2022).
[26] H. Casini and M. Huerta, ”Entanglement entropy in free quantum field theory”, J. Phys. A 42, 504007 (2009).
[27] S. N. Solodukhin, ”Entanglement entropy of black holes”, Living Rev. Rel. 14, (2011)8.
[28] M. Huerta, ”Numerical Determination of the Entanglement Entropy for Free Fields in the Cylinder”, Phys. Lett. B 710, 691 (2012).
[29] D. V. Singh and S. Siwach, ”Thermodynamics of BTZ Black Hole and Entanglement Entropy”, Journal of phys. Conf. Series 481, 012014 (2014).
[30] D. V. Singh and S. Sachan, ”Logarithmic Corrections to the Entropy of Scalar Field in BTZ Black Hole Space-time”, Int. Journal of Mod. Phys. D 26, 1750038 (2017).
[31] M. Cadoni, ”Entanglement entropy of two-dimensional Anti-de Sitter black holes”, Phys. Lett. B 653, 434 (2007).
[32] M. Cadoni and M. Melis, “Holographic entanglement entropy of the BTZ black hole,” Found. Phys. 40, 638 (2010).
[33] M. Cadoni and M. Melis, ”Entanglement Entropy of AdS Black Holes”, Entropy 12, 2244-2267 (2010).
[34] A. Chatterjee and P. Majumdar, ”Black hole entropy: Quantum versus thermal fluctuations”, [arXiv: gr-qc/0303030].
[35] B. Pourhassan, H. Aounallah, M.Faizal, S. Upadhyay, S. Soroushfar, Y. O. Aitenov, S. S. Wani, ”Quantum thermodynamics of an M2-M5 brane system”, JHEP 05, 030 (2022).
[36] B. Pourhassan, S. Upadhyay, ”Perturbed thermodynamics of charged black hole solution in Rastall theory”, Eur. Phys. J. Plus 136, 311 (2021).
[37] S. Upadhyay, B. Pourhassan, ”Logarithmic corrected Van der Waals black holes in higher dimensional AdS space”, Prog. Theor. Exp. Phys. 013B03 (2019).
[38] S. Upadhyay, ”Leading-order corrections to charged rotating AdS black holes thermodynamics”, Gen. Rel. Grav. 50, 128 (2018).
[39] S. Upadhyay, ”Quantum corrections to thermodynamics of quasitopological black holes”, Phys. Lett. B 775, 130 (2017).
[40] S. Upadhyay, B. Pourhassan, H. Farahani, ”P-V criticality of first-order entropy corrected AdS black holes in massive gravity”, Phys. Rev. D 95, 106014 (2017).
[41] B. Pourhassan, M. Faizal, S. Upadhyay, L. A. Asfar, ”Thermal Fluctuations in a Hyperscaling Violation Background”, Eur. Phys. J. C 77, 555 (2017).
[42] A. Strominger, C. Vafa, ”Microscopic Origin of the Bekenstein-Hawking Entropy” Phys. Lett. B 379, 99, (1996).
[43] A. Ashtekar, J. Baez, A. Corichi and K. Krasnov, ”Quantum geometry and black hole entropy”, Phys. Rev. Lett. 80, 904 (1998).
[44] A. Dasgupta, ”Semi-classical quantisation of space-times with apparent horizons”, Class. Quant. Grav. 23, 635 (2006).
[45] S. Das, S. Shankaranarayanan and S. Sur, ”Power-law corrections to entanglement entropy of black holes” Phys. Rev. D 77, 064013 (2008).
[46] D V Singh, ”Power law corrections to BTZ Black hole Entropy” Int. J. Mod. Phys. D 24, 1550001 (2015).
[47] D. V. Singh and S. Siwach ”Scalar Field in BTZ Black Hole Space-time and Entanglement Entropy”, Class. Quantum Grav. 30, 235034 (2013).
[48] D. V. Singh and S. Siwach, ”Fermion Field in BTZ Black Hole Space-time and Entanglement Entropy”, Adv. High Energy Phys. 2015, 528762 (2015).
[49] M Banados, C Teitelboim and J Zanelli, “The Black Hole in Three Dimensional Space-time” Phy. Rev. Lett. 69, 1849 (1992).
[50] R.B.Mann and S.N.Solodukhin, ”Quantum scalar field on three-dimensional (BTZ) black hole instanton: Heat kernel, effective action and thermodynamics”, Phys. Rev. D 55, 3622 (1997).
[51] D. V. Singh and N. K. Singh, ”Anti-Evaporation of Bardeen de-Sitter Black Holes”, Annals Phys. 383, 600-609 (2017).
[52] D. V. Singh, M. S. Ali and S. G. Ghosh, ”Noncommutative geometry inspired rotating black string”, Int. J. Mod. Phys. D 27, 1850108 (2018).
[53] D. V. Singh and S. Siwach, ”On Thermodynamics and Statistical Entropy of Bardeen Black Hole”, [arXiv:1909.11529 [hep-th]].
[54] D. V. Singh, S. Upadhyay and M. S. Ali, ”Rotating Lee–Wick black hole and thermodynamics” Int. J. Mod. Phys. A 37, 2250049 (2022).
[55] D. V. Singh, S. G. Ghosh and S. D. Maharaj, ”Exact nonsingular black holes and thermodynamics”, Nucl. Phys. B 981, 115854 (2022).
[56] D. V. Singh and S. Siwach, ”Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4D Einstein-Gauss-Bonnet Gravity”, Phys. Lett. B 808, 135658 (2020).
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Volume 2, Issue 3
We would like to dedicate this issue to the memory of Prof. M.R. Setare.August 2022Pages 93-100
- Receive Date: 02 July 2022
- Revise Date: 05 August 2022
- Accept Date: 09 August 2022