Motivated by a new interesting nonlinear electrodynamics (NLED) model known as Modification Maxwell (ModMax) theory, we obtain an exact analytic BTZ black hole solution in the presence of a new NLED model and the cosmological constant. Afterward, by considering the obtained solution, we Hawking temperature, entropy, electric charge, mass, and electric potential. We extract the first law of thermodynamics for the BTZ-ModMax black hole. We study thermal stability by evaluating the heat capacity (local stability) and Helmholtz free energy (global stability). By comparing the local and global stabilities, we find the common areas that simultaneously satisfy the local and global stabilities
Heisenberg, W., & Euler, H. (1936). Folgerungen aus der Diracschen Theorie des Positrons. Zeitschrift Für Physik, 98(11–12), 714–732. doi:10.1007/BF01343663.
Schwinger, J. (1951). On gauge invariance and vacuum polarization. Physical Review, 82(5), 664–679. doi:10.1103/PhysRev.82.664.
Heydarzade, Y., Moradpour, H., & Darabi, F. (2017). Black hole solutions in Rastall theory. Canadian Journal of Physics, 95(12), 1253–1256. doi:10.1139/cjp-2017-0254.
Ibrahim, A. I., Safi-Harb, S., Swank, J. H., Parke, W., Zane, S., & Turolla, R. (2002). Discovery of Cyclotron Resonance Features in the Soft Gamma Repeater SGR 1806−20. The Astrophysical Journal, 574(1), L51–L55. doi:10.1086/342366.
Mosquera Cuesta, H. J., & Salim, J. M. (2004). Non-linear electrodynamics and the gravitational redshift of highly magnetized neutron stars. Monthly Notices of the Royal Astronomical Society, 354(4), 55– 59. doi:10.1111/j.1365-2966.2004.08375.x.
Ayon-Beato, E., & Garcia, A. (1999). Non-Singular Charged Black Hole Solution for Non-Linear Source. General Relativity and Gravitation, 31(5), 629–633. doi:10.1023/a:1026640911319.
De Lorenci, V. A., Klippert, R., Novello, M., & Salim, J. M. (2002). Nonlinear electrodynamics and FRW cosmology. Physical Review D, 65(6), 63501. doi:10.1103/PhysRevD.65.063501.
Dymnikova, I. (2004). Regular electrically charged vacuum structures with de Sitter centre in nonlinear electrodynamics coupled to general relativity. Classical and Quantum Gravity, 21(18), 4417–4428. doi:10.1088/0264-9381/21/18/009.
Corda, C., & Cuesta, H. J. M. (2010). Removing black hole singularities with nonlinear electrodynamics. Modern Physics Letters A, 25(28), 2423–2429. doi:10.1142/S0217732310033633.
Born, M., & Infeld, L. (1933). Foundations of the new field theory. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 144(852), 425–451. doi:10.1098/rspa.1934.0059.
Hassaïne, M., & Martínez, C. (2007). Higher-dimensional black holes with a conformally invariant Maxwell source. Physical Review D - Particles, Fields, Gravitation and Cosmology, 75(2), 27502. doi:10.1103/PhysRevD.75.027502.
Maeda, H., Hassaïne, M., & Martínez, C. (2009). Lovelock black holes with a nonlinear Maxwell field. Physical Review D - Particles, Fields, Gravitation and Cosmology, 79(4), 44012. doi:10.1103/PhysRevD.79.044012.
Eslam Panah, B. (2021). Can the power Maxwell nonlinear electrodynamics theory remove the singularity of electric field of point-like charges at their locations? Epl, 134(2), 20005. doi:10.1209/0295-5075/134/20005.
Mazharimousavi, S. H. (2022). Power Maxwell nonlinear electrodynamics and the singularity of the electric field. Modern Physics Letters A, 37(25), 2250170. doi:10.1142/S021773232250170X.
Bandos, I., Lechner, K., Sorokin, D., & Townsend, P. K. (2020). Nonlinear duality-invariant conformal extension of Maxwell’s equations. Physical Review D, 102(12), 121703. doi:10.1103/PhysRevD.102.121703.
Kosyakov, B. P. (2020). Nonlinear electrodynamics with the maximum allowable symmetries. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 810, 135840. doi:10.1016/j.physletb.2020.135840.
Kruglov, S. I. (2021). On generalized ModMax model of nonlinear electrodynamics. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 822, 136633. doi:10.1016/j.physletb.2021.136633.
Kuzenko, S. M., & Raptakis, E. S. N. (2021). Duality-invariant superconformal higher-spin models. Physical Review D, 104(12). doi:10.1103/physrevd.104.125003.
Avetisyan, Z., Evnin, O., & Mkrtchyan, K. (2021). Democratic Lagrangians for Nonlinear Electrodynamics. Physical Review Letters, 127(27), 271601. doi:10.1103/PhysRevLett.127.271601.
Cano, P. A., & Murcia, Á. (2021). Duality-invariant extensions of Einstein-Maxwell theory. Journal of High Energy Physics, 2021(8). doi:10.1007/jhep08(2021)042.
Zhang, M., & Jiang, J. (2021). Conformal scalar NUT-like dyons in conformal electrodynamics. Physical Review D, 104(8), 84094. doi:10.1103/PhysRevD.104.084094.
Flores-Alonso, D., Linares, R., & Maceda, M. (2021). Nonlinear extensions of gravitating dyons: from NUT wormholes to Taub-Bolt instantons. Journal of High Energy Physics, 2021(9), 1–23. doi:10.1007/JHEP09(2021)104.
Bordo, A. B., Kubizňák, D., & Perche, T. R. (2021). Taub-NUT solutions in conformal electrodynamics. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 817, 136312. doi:10.1016/j.physletb.2021.136312.
Bokulić, A., Smolić, I., & Jurić, T. (2022). Constraints on singularity resolution by nonlinear electrodynamics. Physical Review D, 106(6), 64020. doi:10.1103/PhysRevD.106.064020.
Lechner, K., Marchetti, P., Sainaghi, A., & Sorokin, D. (2022). Maximally symmetric nonlinear extension of electrodynamics and charged particles. Physical Review D, 106(1), 16009. doi:10.1103/PhysRevD.106.016009.
Barrientos, J., Cisterna, A., Kubizňák, D., & Oliva, J. (2022). Accelerated black holes beyond Maxwell’s electrodynamics. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 834, 137447. doi:10.1016/j.physletb.2022.137447.
Nastase, H. (2022). Coupling the precursor of the most general theory of electromagnetism invariant under duality and conformal invariance with scalars, and BIon-type solutions. Physical Review D, 105(10), 105024. doi:10.1103/PhysRevD.105.105024.
Babaei-Aghbolagh, H., Babaei Velni, K., Yekta, D. M., & Mohammadzadeh, H. (2022). Emergence of non-linear electrodynamic theories from TT¯-like deformations. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 829, 137079. doi:10.1016/j.physletb.2022.137079.
Babaei-Aghbolagh, H., Velni, K. B., Yekta, D. M., & Mohammadzadeh, H. (2022). Manifestly SL(2, R) Duality-Symmetric Forms in ModMax Theory. Journal of High Energy Physics, 2022(12), 1–16. doi:10.1007/JHEP12(2022)147.
Ferko, C., Smith, L., & Tartaglino-Mazzucchelli, G. (2022). On current-squared flows and ModMax theories. SciPost Physics, 13(2), 12. doi:10.21468/SciPostPhys.13.2.012.
Nomura, K., & Yoshida, D. (2022). Quasinormal modes of charged black holes with corrections from nonlinear electrodynamics. Physical Review D, 105(4), 44006. doi:10.1103/PhysRevD.105.044006.
Pantig, R. C., Mastrototaro, L., Lambiase, G., & Övgün, A. (2022). Shadow, lensing, quasinormal modes, greybody bounds and neutrino propagation by dyonic ModMax black holes. European Physical Journal C, 82(12), 1–25. doi:10.1140/epjc/s10052-022-11125-y.
Panah, B. E. (2024). Analytic Electrically Charged Black Holes in F(R)-ModMax Theory. Progress of Theoretical and Experimental Physics, 2024(2), 023 01. doi:10.1093/ptep/ptae012.
Guzman-Herrera, E., & Breton, N. (2024). Light propagation in the vicinity of the ModMax black hole. Journal of Cosmology and Astroparticle Physics, 2024(1), 41. doi:10.1088/1475-7516/2024/01/041.
Bañados, M., Teitelboim, C., & Zanelli, J. (1992). Black hole in three-dimensional spacetime. Physical Review Letters, 69(13), 1849–1851. doi:10.1103/physrevlett.69.1849.
Witten, E. (2014). Anti-De Sitter Space, Thermal Phase Transition, And Confinement in Gauge Theories. The Oskar Klein Memorial Lectures, 389–419. doi:10.1142/9789814571616_0023.
Lee, H. W., Myung, Y. S., & Kim, J. Y. (1999). Nonpropagation of tachyon on the BTZ black hole in type OB string theory. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 466(2–4), 211–215. doi:10.1016/S0370-2693(99)01121-1.
Larrãaga, A. (2008). On thermodynamical relation between rotating charged BTZ black holes and effective string theory. Communications in Theoretical Physics, 50(6), 1341–1344. doi:10.1088/0253-6102/50/6/19.
Henderson, L. J., Hennigar, R. A., Mann, R. B., Smith, A. R. H., & Zhang, J. (2020). Anti-Hawking phenomena. Physics Letters B, 809, 135732. doi:10.1016/j.physletb.2020.135732.
Campos, L. de S., & Dappiaggi, C. (2021). The anti-Hawking effect on a BTZ black hole with Robin boundary conditions. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 816, 136198. doi:10.1016/j.physletb.2021.136198.
Witten, E. (2007). Three-dimensional gravity revisited. arXiv preprint arXiv:0706.3359. doi:10.48550/arXiv.0706.3359.
Emparan, R., Horowitz, G. T., & Myers, R. C. (2000). Exact description of black holes on branes. Journal of High Energy Physics, 4(1), 1–23. doi:10.1088/1126-6708/2000/01/007.
Carlip, S. (2005). Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole. Classical and Quantum Gravity, 22(12), 85. doi:10.1088/0264-9381/22/12/R01.
Frodden, E., Geiller, M., Noui, K., & Perez, A. (2013). Statistical entropy of a BTZ black hole from loop quantum gravity. Journal of High Energy Physics, 2013(5), 1–17. doi:10.1007/JHEP05(2013)139.
Caputa, P., Jejjala, V., & Soltanpanahi, H. (2014). Entanglement entropy of extremal BTZ black holes. Physical Review D - Particles, Fields, Gravitation and Cosmology, 89(4), 46006. doi:10.1103/PhysRevD.89.046006.
Jurić, T., & Samsarov, A. (2016). Entanglement entropy renormalization for the noncommutative scalar field coupled to classical BTZ geometry. Physical Review D, 93(10), 104033. doi:10.1103/PhysRevD.93.104033.
Emparan, R., Frassino, A. M., & Way, B. (2020). Quantum BTZ black hole. Journal of High Energy Physics, 2020(11), 1–43. doi:10.1007/JHEP11(2020)137.
Germani, C., & Procopio, G. P. (2006). Two-dimensional quantum black holes, branes in Banados-Teitelboim-Zanelli spacetime, and holography. Physical Review D - Particles, Fields, Gravitation and Cosmology, 74(4), 44012. doi:10.1103/PhysRevD.74.044012.
de la Fuente, A., & Sundrum, R. (2014). Holography of the BTZ black hole, inside and out. Journal of High Energy Physics, 2014(9), 1–56. doi:10.1007/JHEP09(2014)073.
Ziogas, V. (2015). Holographic mutual information in global Vaidya-BTZ spacetime. Journal of High Energy Physics, 2015(9), 1–31. doi:10.1007/JHEP09(2015)114.
Cárdenas, M., Fuentealba, O., & Martínez, C. (2014). Three-dimensional black holes with conformally coupled scalar and gauge fields. Physical Review D - Particles, Fields, Gravitation and Cosmology, 90(12), 124072. doi:10.1103/PhysRevD.90.124072.
Zou, D. C., Liu, Y., Wang, B., & Xu, W. (2014). Thermodynamics of rotating black holes with scalar hair in three dimensions. Physical Review D - Particles, Fields, Gravitation and Cosmology, 90(10), 104035. doi:10.1103/PhysRevD.90.104035.
Gwak, B., & Lee, B. H. (2016). Thermodynamics of three-dimensional black holes via charged particle absorption. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 755, 324–327. doi:10.1016/j.physletb.2016.02.028.
Alsaleh, S. (2017). Thermodynamics of BTZ black holes in gravity’s rainbow. International Journal of Modern Physics A, 32(15), 1750076. doi:10.1142/S0217751X17500762.
Gupta, K. S., Jurić, T., & Samsarov, A. (2017). Noncommutative duality and fermionic quasinormal modes of the BTZ black hole. Journal of High Energy Physics, 2017(6), 1–26. doi:10.1007/JHEP06(2017)107.
Lemos, J. P. S., Minamitsuji, M., & Zaslavskii, O. B. (2017). Thermodynamics of extremal rotating thin shells in an extremal BTZ spacetime and the extremal black hole entropy. Physical Review D, 95(4), 44003. doi:10.1103/PhysRevD.95.044003.
Panah, B. E., Hendi, S. H., Panahiyan, S., & Hassaine, M. (2018). BTZ dilatonic black holes coupled to Maxwell and Born-Infeld electrodynamics. Physical Review D, 98(8), 84006. doi:10.1103/PhysRevD.98.084006.
Nashed, G. G. L., & Capozziello, S. (2018). Charged anti-de Sitter BTZ black holes in Maxwell- f (T) gravity. International Journal of Modern Physics A, 33(13), 1850076. doi:10.1142/S0217751X18500768.
Hong, S. T., Kim, Y. W., & Park, Y. J. (2019). Local free-fall temperatures of charged BTZ black holes in massive gravity. Physical Review D, 99(2), 24047. doi:10.1103/PhysRevD.99.024047.
Mu, B., Tao, J., & Wang, P. (2020). Free-fall rainbow BTZ black hole. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 800, 135098. doi:10.1016/j.physletb.2019.135098.
Xu, Z. M., Wu, B., & Yang, W. L. (2020). Diagnosis inspired by the thermodynamic geometry for different thermodynamic schemes of the charged BTZ black hole. European Physical Journal C, 80(10), 1–10. doi:10.1140/epjc/s10052-020-08563-x.
Cañate, P., Magos, D., & Breton, N. (2020). Nonlinear electrodynamics generalization of the rotating BTZ black hole. Physical Review D, 101(6), 64010. doi:10.1103/PhysRevD.101.064010.
Huang, Y., & Tao, J. (2022). Thermodynamics and phase transition of BTZ black hole in a cavity. Nuclear Physics B, 982, 115881. doi:10.1016/j.nuclphysb.2022.115881.
Eslam Panah, B. (2023). Charged Accelerating BTZ Black Holes. Fortschritte Der Physik, 71(8–9), 2300012. doi:10.1002/prop.202300012.
Karakasis, T., Koutsoumbas, G., & Papantonopoulos, E. (2023). Black holes with scalar hair in three dimensions. Physical Review D, 107(12), 124047. doi:10.1103/PhysRevD.107.124047.
Panah, B. E., Khorasani, M., & Sedaghat, J. (2023). Three-dimensional accelerating AdS black holes in F(R) gravity. European Physical Journal Plus, 138(8), 1–10. doi:10.1140/epjp/s13360-023-04339-w.
Cvetič, M., & Gubser, S. S. (1999). Phases of R-charged black holes, spinning branes and strongly coupled gauge theories. Journal of High Energy Physics, 3(4), 24. doi:10.1088/1126-6708/1999/04/024.
Caldarelli, M. M., Cognola, G., & Klemm, D. (2000). Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories. Classical and Quantum Gravity, 17(2), 399–420. doi:10.1088/0264-9381/17/2/310.
Eslam Panah, B. (2024). Thermodynamics and Thermal Stability of BTZ-ModMax Black Holes. Contributions of Science and Technology for Engineering, 1(3), 25-34. doi: 10.22080/cste.2024.5112
MLA
Behzad Eslam Panah. "Thermodynamics and Thermal Stability of BTZ-ModMax Black Holes", Contributions of Science and Technology for Engineering, 1, 3, 2024, 25-34. doi: 10.22080/cste.2024.5112
HARVARD
Eslam Panah, B. (2024). 'Thermodynamics and Thermal Stability of BTZ-ModMax Black Holes', Contributions of Science and Technology for Engineering, 1(3), pp. 25-34. doi: 10.22080/cste.2024.5112
CHICAGO
B. Eslam Panah, "Thermodynamics and Thermal Stability of BTZ-ModMax Black Holes," Contributions of Science and Technology for Engineering, 1 3 (2024): 25-34, doi: 10.22080/cste.2024.5112
VANCOUVER
Eslam Panah, B. Thermodynamics and Thermal Stability of BTZ-ModMax Black Holes. Contributions of Science and Technology for Engineering, 2024; 1(3): 25-34. doi: 10.22080/cste.2024.5112