The GUP effect on tunneling of massive vector bosons from the 2+1 dimensional black hole. (English) Zbl 1404.83047
Summary: In this study, the Generalized Uncertainty Principle (GUP) effect on the Hawking radiation formed by tunneling of a massive vector boson particle from the 2+1 dimensional new-type black hole was investigated. We used modified massive vector boson equation based on the GUP. Then, the Hamilton-Jacobi quantum tunneling approach was used to work out the tunneling probability of the massive vector boson particle and Hawking temperature of the black hole. Due to the GUP effect, the modified Hawking temperature was found to depend on the black hole properties, on the AdS radius, and on the energy, mass, and total angular momentum of the tunneling massive vector boson. In the light of these results, we also observed that modified Hawking temperature increases by the total angular momentum of the particle while it decreases by the energy and mass of the particle and the graviton mass. Also, in the context of the GUP, we see that the Hawking temperature due to the tunneling massive vector boson is
completely different from both that of the spin-0 scalar and that of the spin-1/2 Dirac particles obtained in the previous study. We also calculate the heat capacity of the black hole using the modified Hawking temperature and then discuss influence of the GUP on the stability of the black hole.
MSC:
| 83C57 | Black holes |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 83C80 | Analogues of general relativity in lower dimensions |
References:
| [1] | Hawking, S. W., Black hole explosions?, Nature, 248, 30-31, (1974) · Zbl 1370.83053 · doi:10.1038/248030a0 |
| [2] | Hawking, S. W., Particle creation by black holes, Communications in Mathematical Physics, 43, 3, 199-220, (1975) · Zbl 1378.83040 · doi:10.1007/BF02345020 |
| [3] | Hawking, S. W., Black holes and thermodynamics, Physical Review D: Particles, Fields, Gravitation and Cosmology, 13, 2, 191-197, (1976) · doi:10.1103/physrevd.13.191 |
| [4] | Bardeen, J. M.; Carter, B.; Hawking, S. W., The four laws of black hole mechanics, Communications in Mathematical Physics, 31, 161-170, (1973) · Zbl 1125.83309 · doi:10.1007/BF01645742 |
| [5] | Robinson, S. P.; Wilczek, F., Relationship between Hawking radiation and gravitational anomalies, Physical Review Letters, 95, (2005) · doi:10.1103/physrevlett.95.011303 |
| [6] | Giddings, S. B., High-energy black hole production, AIP Conference Proceedings, 957, 1, 69, (2007) · Zbl 1181.83114 · doi:10.1063/1.2823829 |
| [7] | Kraus, P.; Wilczek, F., Effect of self-interaction on charged black hole radiance, Nuclear Physics B, 437, 1, 231-242, (1995) · doi:10.1016/0550-3213(94)00588-6 |
| [8] | Kraus, P.; Wilczek, F., Self-interaction correction to black hole radiance, Nuclear Physics B, 433, 2, 403-420, (1995) · doi:10.1016/0550-3213(94)00411-7 |
| [9] | Parikh, M. K.; Wilczek, F., Hawking radiation as tunneling, Physical Review Letters, 85, 24, 5042-5045, (2000) · Zbl 1369.83053 · doi:10.1103/PhysRevLett.85.5042 |
| [10] | Kerner, R.; Mann, R. B., Tunnelling, temperature, and Taub-NUT black holes, Physical Review D: Particles, Fields, Gravitation and Cosmology, 73, (2006) · doi:10.1103/PhysRevD.73.104010 |
| [11] | Kerner, R.; Mann, R. B., Fermions tunnelling from black holes, Classical and Quantum Gravity, 25, 9, (2008) · Zbl 1140.83377 · doi:10.1088/0264-9381/25/9/095014 |
| [12] | Chen, D. Y.; Jiang, Q. Q.; Zu, X. T., Fermions tunnelling from the charged dilatonic black holes, Classical and Quantum Gravity, 25, (2008) · Zbl 1152.83012 · doi:10.1088/0264-9381/25/20/205022 |
| [13] | Zhang, J.; Zhao, Z., Charged particles’ tunnelling from the Kerr–Newman black hole, Physics Letters B, 638, 2-3, 110-113, (2006) · Zbl 1248.83091 · doi:10.1016/j.physletb.2006.05.059 |
| [14] | Huang, J.; Liu, W., Fermion tunneling from an axis-symmetric black hole beyond the semiclassical approximation, International Journal of Theoretical Physics, 49, 10, 2621-2629, (2010) · Zbl 1201.83032 · doi:10.1007/s10773-010-0453-8 |
| [15] | Zeng, X. X.; Li, Q., On particles tunneling from the Taub-NUT-AdS black hole, Chinese Physics B, 18, 11, 4716-4720, (2009) · doi:10.1088/1674-1056/18/11/018 |
| [16] | Criscienzo, R. R.; Vanzo, L. L., Fermion tunneling from dynamical horizons, Europhysics Letters, 82, 6, (2008) · doi:10.1209/0295-5075/82/60001 |
| [17] | Chen, D. Y.; Jian, Q. Q.; Zu, X. T., Hawking radiation of Dirac particles via tunnelling from rotating black holes in de Sitter spaces, Physics Letters B, 665, 2-3, 106-110, (2008) · Zbl 1328.83082 · doi:10.1016/j.physletb.2008.05.064 |
| [18] | Jian, Q. Q., Dirac particle tunneling from black rings, Physical Review D: Particles, Fields, Gravitation and Cosmology, 78, (2008) · doi:10.1103/PhysRevD.78.044009 |
| [19] | Li, R.; Zhao, J.-K.; Wu, X.-H., Tunneling radiation of massive vector bosons from dilaton black holes, Communications in Theoretical Physics, 66, 1, 77-83, (2016) · Zbl 1345.83019 · doi:10.1088/0253-6102/66/1/077 |
| [20] | Li, R.; Ren, J.-R., Dirac particles tunneling from BTZ black hole, Physics Letters B, 661, 5, 370-372, (2008) · Zbl 1282.83035 · doi:10.1016/j.physletb.2008.01.077 |
| [21] | Li, H.; Yang, S.; Jiang, Q.; Qi, D., Charged particle’s tunneling radiation from the charged BTZ black hole, Physics Letters B, 641, 2, 139-144, (2006) · Zbl 1248.83072 · doi:10.1016/j.physletb.2006.08.033 |
| [22] | Kruglov, S. I., Black hole radiation of spin-1 particles in (1+2) dimensions, Modern Physics Letters A, 29, 39, (2014) · Zbl 1308.83095 · doi:10.1142/S0217732314502034 |
| [23] | Gursel, H.; Sakalli, I., Hawking radiation of massive vector particles from a warped AdS_{3} black hole, Canadian Journal of Physics, 94, 2, 147-149, (2016) · doi:10.1139/cjp-2015-0495 |
| [24] | Sakalli, I.; Ovgun, A., Hawking radiation of spin-1 particles from a three-dimensional rotating hairy black hole, Journal of Experimental and Theoretical Physics, 121, 3, 404-407, (2015) · doi:10.1134/S1063776115090113 |
| [25] | Chen, G.-R.; Zhou, S.; Huang, Y.-C., Vector particles tunneling from BTZ black holes, International Journal of Modern Physics D, 24, 1, (2015) · Zbl 1308.83082 · doi:10.1142/S0218271815500054 |
| [26] | Chen, G. R.; Huang, Y. C., Hawking radiation of vector particles as tunneling from the apparent horizon of Vaidya black holes, International Journal of Modern Physics A, 30, 15, (2015) · Zbl 1320.83035 · doi:10.1142/S0217751X15500839 |
| [27] | Li, X.-Q.; Chen, G.-R., Massive vector particles tunneling from Kerr and Kerr–Newman black holes, Physics Letters B, 751, 34-38, (2015) · Zbl 1360.83038 · doi:10.1016/j.physletb.2015.10.007 |
| [28] | Sakalli, I.; Övgün, A., Quantum tunneling of massive spin-1 particles from non-stationary metrics, General Relativity and Gravitation, 48, article 1, (2016) · Zbl 1332.83068 · doi:10.1007/s10714-015-1997-y |
| [29] | Chen, G.-R.; Zhou, S.; Huang, Y.-C., Vector particles tunneling from four-dimensional Schwarzschild black holes, Astrophysics and Space Science, 357, article 51, (2015) · doi:10.1007/s10509-015-2259-x |
| [30] | Li, R.; Zhao, J., Hawking radiation of massive vector particles from the linear dilaton black holes, The European Physical Journal Plus, 131, article 249, (2016) · doi:10.1140/epjp/i2016-16249-5 |
| [31] | Sakalli, I.; Gursel, H., Quantum tunneling from rotating black holes with scalar hair in three dimensions, The European Physical Journal C, 76, 6, article 318, (2016) · doi:10.1140/epjc/s10052-016-4158-x |
| [32] | Gecim, G.; Sucu, Y., Tunnelling of relativistic particles from new type black hole in new massive gravity, Journal of Cosmology and Astroparticle Physics, 2013, 2, article 023, (2013) · doi:10.1088/1475-7516/2013/02/023 |
| [33] | Gecim, G.; Sucu, Y., Dirac and scalar particles tunnelling from topological massive warped-AdS_{3} black hole, Astrophysics and Space Science, 357, article 105, (2015) · doi:10.1007/s10509-015-2332-5 |
| [34] | Gecim, G.; Sucu, Y., Massive vector bosons tunnelled from the (2+1)-dimensional black holes, The European Physical Journal Plus, 132, article 105, (2017) · doi:10.1140/epjp/i2017-11391-2 |
| [35] | Townsend, P. K., Small-scale structure of spacetime as the origin of the gravitational constant, Physical Review D: Particles, Fields, Gravitation and Cosmology, 15, article 2795, (1977) · doi:10.1103/physrevd.15.2795 |
| [36] | Amati, D.; Ciafaloni, M.; Veneziano, G., Can spacetime be probed below the string size?, Physics Letters B, 216, 1-2, 41-47, (1989) · doi:10.1016/0370-2693(89)91366-X |
| [37] | Konishi, K.; Paffuti, G.; Provero, P., Minimum physical length and the generalized uncertainty principle in string theory, Physics Letters B, 234, 3, 276-284, (1990) · doi:10.1016/0370-2693(90)91927-4 |
| [38] | Garay, L. J., Quantum gravity and minimum length, International Journal of Modern Physics A, 10, 2, 145-166, (1995) · doi:10.1142/S0217751X95000085 |
| [39] | Kempf, A.; Mangano, G., Minimal length uncertainty relation and ultraviolet regularization, Physical Review D: Particles, Fields, Gravitation and Cosmology, 55, 12, article 7909, (1997) · doi:10.1103/physrevd.55.7909 |
| [40] | Ali, A. F.; Khalil, M. M.; Vagenas, E. C., Minimal length in quantum gravity and gravitational measurements, EPL (Europhysics Letters), 112, 2, (2015) · doi:10.1209/0295-5075/112/20005 |
| [41] | Tawfik, A. N.; Diab, A. M., A review of the generalized uncertainty principle, Reports on Progress in Physics, 78, 12, (2015) · doi:10.1088/0034-4885/78/12/126001 |
| [42] | Tawfik, A.; Diab, A., Effect of the generalized uncertainty principle on compact stars, International Journal of Modern Physics D: Gravitation, Astrophysics, Cosmology, 23, 10, 161-170, (2014) · Zbl 1305.81005 · doi:10.1142/S0218271814300250 |
| [43] | Maggiore, M., A Generalized Uncertainty Principle in Quantum Gravity, Physics Letters B, 304, 1-2, 65-69, (1993) · doi:10.1016/0370-2693(93)91401-8 |
| [44] | Scardigli, F., Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment, Physics Letters B, 452, 1-2, 39-44, (1999) · doi:10.1016/S0370-2693(99)00167-7 |
| [45] | Ghaneh, T.; Darabi, F.; Motavalli, H., Signature change by gup, International Journal of Modern Physics D, 22, 5, (2013) · Zbl 1267.83118 · doi:10.1142/S0218271813500260 |
| [46] | Brau, F., Minimal length uncertainty relation and the hydrogen atom, Journal of Physics A: Mathematical and Theoretical, 32, 44, 7691-7696, (1999) · Zbl 0991.81047 · doi:10.1088/0305-4470/32/44/308 |
| [47] | Pedram, P.; Amirfakhrian, M.; Shababi, H., On the (2 + 1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty, International Journal of Modern Physics D, 24, 2, (2015) · Zbl 1311.81120 · doi:10.1142/S0218271815500169 |
| [48] | Nozari, K.; Akhshabi, S.; Mod, J., Effects of the generalized uncertainty principle on the inflation parameters, International Journal of Modern Physics D, 19, 5, 513-521, (2010) · Zbl 1193.83069 · doi:10.1142/S0218271810016543 |
| [49] | Vakili, B., Cosmology with minimal length uncertainty relations, International Journal of Modern Physics D, 18, 7, 1059-1071, (2009) · Zbl 1168.83347 · doi:10.1142/S0218271809014935 |
| [50] | Ali, A. F.; Majumder, B., Towards a cosmology with minimal length and maximal energy, Classical and Quantum Gravity, 31, 21, (2014) · Zbl 1304.83020 · doi:10.1088/0264-9381/31/21/215007 |
| [51] | Majumder, B., \(f(R)\) in holographic and agegraphic dark energy models and the generalized uncertainty principle, Advances in High Energy Physics, 2013, 1-11, (2013) · Zbl 1328.83144 · doi:10.1155/2013/143195 |
| [52] | Sadeghi, J.; Shajiee, V. R., Quantum tunneling from the charged non-rotating BTZ black hole with GUP, The European Physical Journal Plus, 132, article 132, (2017) · doi:10.1140/epjp/i2017-11432-x |
| [53] | Myung, Y. S.; Kim, Y.-W.; Park, Y.-J., Black hole thermodynamics with generalized uncertainty principle, Physics Letters B, 645, 5-6, 393-397, (2007) · Zbl 1273.83106 · doi:10.1016/j.physletb.2006.12.062 |
| [54] | Ali, A. F.; Moussa, M., Towards thermodynamics with generalized uncertainty principle, Advances in High Energy Physics, 2014, 1-7, (2014) · Zbl 1425.81063 · doi:10.1155/2014/629148 |
| [55] | Jana, T. K.; Roy, P., Exact solution of the Klein–Gordon equation in the presence of a minimal length, Physics Letters A, 373, 14, 1239-1241, (2009) · Zbl 1228.81154 · doi:10.1016/j.physleta.2009.02.007 |
| [56] | Nozari, K.; Karami, M., Minimal length and generalized Dirac equation, Modern Physics Letters A, 20, 40, 3095-3103, (2005) · Zbl 1082.83509 · doi:10.1142/S0217732305018517 |
| [57] | Li, X.-Q., Massive vector particles tunneling from black holes influenced by the generalized uncertainty principle, Physics Letters B, 763, 80-86, (2016) · Zbl 1370.83055 · doi:10.1016/j.physletb.2016.10.032 |
| [58] | Nozari, K.; Saghafi, S., Natural cutoffs and quantum tunneling from black hole horizon, Journal of High Energy Physics, 5, (2012) · doi:10.1007/JHEP11(2012)005 |
| [59] | Chen, D.; Wu, H.; Yang, H., Fermion’s tunnelling with effects of quantum gravity, Advances in High Energy Physics, 2013, 1-6, (2013) · Zbl 1328.81245 · doi:10.1155/2013/432412 |
| [60] | Chen, D. Y.; Jiang, Q. Q.; Wang, P.; Yang, H., Remnants, fermions’ tunnelling and effects of quantum gravity, Journal of High Energy Physics, 176, (2013) · Zbl 1342.83143 · doi:10.1007/JHEP11(2013)176 |
| [61] | Chen, D.; Wu, H.; Yang, H.; Yang, S., Effects of quantum gravity on black holes, International Journal of Modern Physics A, 29, 26, (2014) · Zbl 1301.83020 · doi:10.1142/S0217751X14300543 |
| [62] | Zeng, X.-X.; Chen, Y., Quantum gravity corrections to fermions’ tunnelling radiation in the Taub-NUT spacetime, General Relativity and Gravitation, 47, article 47, (2015) · Zbl 1317.83039 · doi:10.1007/s10714-015-1890-8 |
| [63] | Li, H. L.; Feng, Z. W.; Zu, X. T., Quantum tunneling from high dimensional Gödel black hole, General Relativity and Gravitation, 48, article 18, (2016) · Zbl 1334.83050 · doi:10.1007/s10714-015-2015-0 |
| [64] | Wang, P.; Yang, H.; Ying, S., Quantum gravity corrections to the tunneling radiation of scalar particles, International Journal of Theoretical Physics, 55, 5, 2633-2642, (2016) · Zbl 1338.83125 · doi:10.1007/s10773-015-2898-2 |
| [65] | Liu, Z.-Y.; Ren, J.-R., Fermions tunnelling with quantum gravity correction, Communications in Theoretical Physics, 62, 6, 819-823, (2014) · Zbl 1308.83110 · doi:10.1088/0253-6102/62/6/08 |
| [66] | Mu, B.; Wang, P.; Yang, H., Minimal length effects on tunnelling from spherically symmetric black holes, Advances in High Energy Physics, 2015, 1-8, (2015) · Zbl 1375.83032 · doi:10.1155/2015/898916 |
| [67] | Li, G.; Zu, X., Scalar particles’ tunneling and effect of quantum gravity, Journal of Applied Mathematics and Physics, 3, 2, 134-139, (2015) · doi:10.4236/jamp.2015.32020 |
| [68] | Anacleto, M. A.; Brito, F. A.; Passos, E., Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP, Physics Letters B, 749, 181-186, (2015) · Zbl 1364.83016 · doi:10.1016/j.physletb.2015.07.072 |
| [69] | Li, H.; Zu, X., Black hole remnant and quantum tunnelling in three-dimensional Gödel spacetime, Astrophysics and Space Science, 357, article 6, (2015) · doi:10.1007/s10509-015-2316-5 |
| [70] | Sakalli, I.; Övgün, A.; Jusufi, K., GUP assisted Hawking radiation of rotating acoustic black holes, Astrophysics and Space Science, 361, article 330, (2016) · doi:10.1007/s10509-016-2922-x |
| [71] | Vagenas, E. C.; Alsaleh, S. M.; Ali, A. F., GUP parameter and black-hole temperature, EPL (Europhysics Letters), 120, 4, (2017) · doi:10.1209/0295-5075/120/40001 |
| [72] | Gecim, G.; Sucu, Y., The GUP effect on Hawking radiation of the 2+1 dimensional black hole, Physics Letters B, 773, 391-394, (2017) · Zbl 1378.83039 · doi:10.1016/j.physletb.2017.08.053 |
| [73] | Gecim, G.; Sucu, Y., Quantum gravity effect on the tunneling particles from 2 + 1-dimensional new-type black hole, Advances in High Energy Physics, 2018, 1-7, (2018) · Zbl 1404.83048 · doi:10.1155/2018/8728564 |
| [74] | Dernek, M.; Gurtas Dogan, S.; Sucu, Y.; Unal, N., Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime |
| [75] | Tekincay, C.; Sucu, Y., Photon in a cylindrical resonant cavity, Turkish Journal of Physics, 42, 175-182, (2018) · doi:10.3906/fiz-1708-16 |
| [76] | Sucu, Y.; Ünal, N., Vector bosons in the expanding universe, The European Physical Journal C, 44, 2, 287-291, (2005) · doi:10.1140/epjc/s2005-02356-0 |
| [77] | Barut, A. O., Excited states of zitterbewegung, Physics Letters B, 237, 3-4, 436-439, (1990) · doi:10.1016/0370-2693(90)91202-M |
| [78] | Unal, N., Kernel of the classical zitterbewegung, Foundations of Physics, 27, 5, 747-758, (1997) · doi:10.1007/BF02550174 |
| [79] | Ünal, N., A simple model of the classical zitterbewegung: photon wave function, Foundations of Physics, 27, 5, 731-746, (1997) · doi:10.1007/BF02550173 |
| [80] | Ünal, N., Path integral quantization of a spinning particle, Foundations of Physics. An International Journal Devoted to the Conceptual Bases and Fundamental Theories of Modern Physics, 28, 5, 755-762, (1998) · doi:10.1023/A:1018897719975 |
| [81] | Sucu, Y.; Unal, N., International Journal of Modern Physics A, 17, 8, 1137-1147, (2002) · Zbl 1009.81054 · doi:10.1142/S0217751X02005852 |
| [82] | Sucu, Y.; Ünal, N., Symmetry and integrability in the classical model of Zitterbewegung, Foundations of Physics, 42, 8, 1067-1077, (2012) · Zbl 1262.81051 · doi:10.1007/s10701-012-9648-6 |
| [83] | Castro, L. B.; de Castro, A. S., Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations, Physical review A, 90, (2014) · doi:10.1103/PhysRevA.90.022101 |
| [84] | Unal, N., Duffin-Kemmer-Petiau equation, proca equation and Maxwells equation in 1+1 D, Concepts of Physics, 2, 273-282, (2005) |
| [85] | Sucu, Y.; Ünal, N., Exact solution of Dirac equation in 2+1 dimensional gravity, Journal of Mathematical Physics, 48, 5, (2007) · Zbl 1144.81415 · doi:10.1063/1.2735442 |
| [86] | Kempf, A.; Mangano, G.; Mann, R. B., Hilbert space representation of the minimal length uncertainty relation, Physical Review D: Particles, Fields, Gravitation and Cosmology, 52, 2, 1108-1118, (1995) · doi:10.1103/PhysRevD.52.1108 |
| [87] | Hossenfelder, S.; Bleicher, M.; Hofmann, S.; Ruppert, J.; Scherer, S.; Stöcker, H., Signatures in the Planck regime, Physics Letters B, 575, 1-2, 85-99, (2003) · Zbl 1029.83501 · doi:10.1016/j.physletb.2003.09.040 |
| [88] | Feng, Z. W.; Li, H. L.; Zu, X. T.; Yang, S. Z., Quantum corrections to the thermodynamics of Schwarzschild–Tangherlini black hole and the generalized uncertainty principle, The European Physical Journal C, 76, article 212, (2016) · doi:10.1140/epjc/s10052-016-4057-1 |
| [89] | Li, Z. H.; Zhang, L. M., Fermions tunnelling from black string and Kerr AdS black hole with consideration of quantum gravity, International Journal of Theoretical Physics, 55, 1, 401-411, (2016) · Zbl 1337.83040 · doi:10.1007/s10773-015-2674-3 |
| [90] | Deser, S.; Jackiw, R.; Templeton, S., Three-dimensional massive gauge theories, Physical Review Letters, 48, 15, 975-978, (1982) · doi:10.1103/PhysRevLett.48.975 |
| [91] | Deser, S.; Jackiw, R.; ’t Hooft, G., Three-dimensional Einstein gravity: dynamics of flat space, Annals of Physics, 152, 1, 220-235, (1984) · doi:10.1016/0003-4916(84)90085-x |
| [92] | Witten, E., 2 + 1 dimensional gravity as an exactly soluble system, Nuclear Physics B, 311, 1, 46-78, (1988) · Zbl 1258.83032 · doi:10.1016/0550-3213(88)90143-5 |
| [93] | Banados, M.; Teitelboim, C.; Zanelli, J., Black hole in three-dimensional spacetime, Physical Review Letters, 69, 13, 1849-1851, (1992) · Zbl 0968.83514 · doi:10.1103/PhysRevLett.69.1849 |
| [94] | Bergshoeff, E. A.; Hohm, O.; Townsend, P. K., Massive gravity in three dimensions, Physical Review Letters, 102, 20, (2009) · doi:10.1103/physrevlett.102.201301 |
| [95] | Ahmedov, H.; Aliev, A. N., Type D solutions of 3D new massive gravity, Physical Review D: Particles, Fields, Gravitation and Cosmology, 83, 8, (2011) · doi:10.1103/PhysRevD.83.084032 |
| [96] | Bakas, I.; Sourdis, C., Homogeneous vacua of (generalized) new massive gravity, Classical and Quantum Gravity, 28, 1, (2011) · Zbl 1207.83044 · doi:10.1088/0264-9381/28/1/015012 |
| [97] | Oliva, J.; Tempo, D.; Troncoso, R., Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity, Journal of High Energy Physics, 2009, 07, article 011, (2009) · doi:10.1088/1126-6708/2009/07/011 |
| [98] | Oliva, J.; Tempo, D.; Troncoso, R., Static spherically symmetric solutions for conformal gravity in three dimensions, International Journal of Modern Physics A, 24, 08n09, article 1588, (2009) · Zbl 1170.83503 · doi:10.1142/S0217751X09045054 |
| [99] | Kwon, Y.; Nam, S.; Park, J.-D.; Yi, S.-H., Quasi-normal modes for new type black holes in new massive gravity, Classical and Quantum Gravity, 28, 14, (2011) · Zbl 1222.83109 · doi:10.1088/0264-9381/28/14/145006 |
| [100] | Gonzalez, P. A.; Vazquez, Y., Dirac quasinormal modes of new type black holes in new massive gravity, European Physical Journal C, 74, article 2969, (2014) · doi:10.1140/epjc/s10052-014-2969-1 |
| [101] | Cai, R.-G.; Cao, L.-M.; Ohta, N., Thermodynamics of black holes in Hořava–Lifshitz gravity, Physics Letters B, 5, 504-509, (679) · doi:10.1016/j.physletb.2009.07.075 |
| [102] | Dehghani, M., Thermodynamics of (2+1)-dimensional charged black holes with power-law Maxwell field, Physical Review D, 94, (2016) · doi:10.1103/PhysRevD.94.104071 |
| [103] | Hendi, S. H.; Panahiyan, S.; Panah, B. E., Geometrical method for thermal instability of nonlinearly charged BTZ black holes, Advances in High Energy Physics, 2015, 1-12, (2015) · Zbl 1366.83043 · doi:10.1155/2015/743086 |
| [104] | Miao, Y.-G.; Wu, Y.-M., Thermodynamics of the Schwarzschild-AdS black hole with a minimal length, Advances in High Energy Physics, 2017, 1-14, (2017) · Zbl 1366.83056 · doi:10.1155/2017/1095217 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
