×
Chowdhury, Sourav Roy; Deb, Debabrata; Rahaman, Farook; Ray, Saibal; Guha, B. K.

Noncommutative black hole in the Finslerian spacetime. (English) Zbl 1482.83108

Classical Quantum Gravity 38, No. 14, Article ID 145019, 16 p. (2021).
Summary: We study the behavior of the noncommutative radiating Schwarzschild black hole in the Finslerian spacetime. The investigation shows that black hole possesses either (i) two horizons, or (ii) a single horizon, or (iii) no horizon corresponding to a minimal mass. We obtain that the minimal mass significantly changes with the Finslerian parameter, keeping minimal horizon remain unchanged. It turns out that under Finslerian spacetime, the maximum temperature before cooling down to absolute zero varies with the Finslerian parameter. We then study the stability of the black hole by analyzing the specific heat and free energy. The energy conditions, their violation limit also scrutinized. Our findings suggest a stable black hole remnant, whose mass and size are uniquely determined in terms of the Finslerian parameter \(\overline{\mathrm{Ric}}\) and noncommutative parameter \(\chi\). The physical relevance of these results are discussed in a brief.

Cited in 2 Documents

MSC:

83C65 Methods of noncommutative geometry in general relativity
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C57 Black holes
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
80A10 Classical and relativistic thermodynamics

Keywords:

noncommutative geometry; Finslerian spacetime; blackhole; numerical relativity
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Hawking, S. W., Nature, 248, 30 (1974) · Zbl 1370.83053 · doi:10.1038/248030a0
[2] Hawking, S. W., Commun. Math. Phys., 43, 199 (1975) · Zbl 1378.83040 · doi:10.1007/bf02345020
[3] Bekenstein, J. D., Phys. Rev. D, 7, 2333 (1973) · Zbl 1369.83037 · doi:10.1103/physrevd.7.2333
[4] Bekenstein, J. D., Phys. Rev. D, 9, 3292 (1974) · doi:10.1103/physrevd.9.3292
[5] Aharonov, Y.; Casher, A.; Nussinov, S., Phys. Lett. B, 191, 51 (1987) · doi:10.1016/0370-2693(87)91320-7
[6] Susskind, L.; Thorlacius, L., Nucl. Phys. B, 382, 123 (1992) · doi:10.1016/0550-3213(92)90081-l
[7] Susskind, L., Phys. Rev. Lett., 71, 2367 (1993) · Zbl 0972.83565 · doi:10.1103/physrevlett.71.2367
[8] Witten, E., Nucl. Phys. B, 460, 335 (1996) · Zbl 1003.81527 · doi:10.1016/0550-3213(95)00610-9
[9] Seiberg, N.; Witten, E., J. High Energy Phys. (1999) · Zbl 0957.81085 · doi:10.1088/1126-6708/1999/09/032
[10] Snyder, H. S., Phys. Rev., 71, 38 (1947) · Zbl 0035.13101 · doi:10.1103/physrev.71.38
[11] Gruppuso, A., J. Phys. A: Math. Gen., 38, 2039 (2005) · Zbl 1073.81054 · doi:10.1088/0305-4470/38/9/014
[12] Nicolini, P., J. Phys. A: Math. Gen., 38, L631 (2005) · Zbl 1081.83020 · doi:10.1088/0305-4470/38/39/l02
[13] Smailagic, A.; Spallucci, E., Feynman path integral on the non-commutative plane, J. Phys. A: Math. Gen., 36, L467 (2003) · Zbl 1042.81044 · doi:10.1088/0305-4470/36/33/101
[14] Smailagic, A.; Spallucci, P., UV divergence-free QFT on noncommutative plane., J. Phys. A: Math. Gen., 36 (2003) · Zbl 1041.81593 · doi:10.1088/0305-4470/36/45/C01
[15] Cho, S.; Hinterding, R.; Madore, J.; Steinacker, H., Int. J. Mod. Phys. D, 09, 161 (2000) · Zbl 0961.81121 · doi:10.1142/s0218271800000153
[16] Smailagic, A.; Spallucci, E., J. Phys. A: Math. Gen., 37, 7169 (2004) · Zbl 1062.81138 · doi:10.1088/0305-4470/37/28/008
[17] Mocioiu, I.; Pospelov, M.; Roiban, R., Phys. Lett. B, 489, 390 (2000) · Zbl 1031.81664 · doi:10.1016/s0370-2693(00)00928-x
[18] Chaichian, M.; Sheikh-Jabbari, M. M.; Tureanu, A., Phys. Rev. Lett., 86, 2716 (2001) · doi:10.1103/physrevlett.86.2716
[19] Carroll, S. M.; Harvey, J. A.; Kosteleck, V. A.; Lane, C. D.; Okamoto, T., Phys. Rev. Lett., 87 (2001) · doi:10.1103/physrevlett.87.141601
[20] Ho, P. M.; Kao, H. C., Phys. Rev. Lett., 88 (2002) · doi:10.1103/physrevlett.88.151602
[21] Adorno, T. C.; Gitman, D. M.; Shabad, A. E.; Vassilavich, D. V., Phys. Rev. D, 84, 84085031 (2011) · doi:10.1103/physrevd.84.065003
[22] Stern, A., Phys. Rev. Lett., 100 (2008) · Zbl 1228.81195 · doi:10.1103/physrevlett.100.061601
[23] Vacaru, S. I., Class. Quantum Grav., 27 (2010) · Zbl 1190.83067 · doi:10.1088/0264-9381/27/10/105003
[24] Connes, A., Commun. Math. Phys., 182, 155 (1996) · Zbl 0881.58009 · doi:10.1007/bf02506388
[25] López, E., J. Phys. A: Math. Gen., 27, 845 (1994) · Zbl 0818.17013 · doi:10.1088/0305-4470/27/3/025
[26] Madore, J., An introduction to Noncommutative Differential Geometry and its Physical Applications (1995), Cambridge: Cambridge University Press, Cambridge · Zbl 0842.58002
[27] Heller, M.; Sasin, W., J. Math. Phys., 37, 2665 (1996) · Zbl 0866.58010 · doi:10.1063/1.531733
[28] Heller, M., Acta Cosmol., 18, 31 (1992)
[29] Heller, G.; Lambert, D.; Madore, J., Arthroskopie, 11, 51 (1998) · doi:10.1007/s001420050009
[30] Castorina, P.; Zappalá, D., AIP Conf. Proc., 756, 460 (2005) · doi:10.1063/1.1921025
[31] Schreck, M., J. Phys.: Conf. Ser., 563 (2014) · doi:10.1088/1742-6596/563/1/012026
[32] Nicolini, P.; Smailagic, A.; Spallucci, E., Phys. Lett. B, 632, 547 (2006) · Zbl 1247.83113 · doi:10.1016/j.physletb.2005.11.004
[33] Smailagic, A.; Spallucci, E., J. Phys. A: Math. Gen., 35, L363 (2002) · Zbl 1066.81576 · doi:10.1088/0305-4470/35/26/103
[34] Myung, Y. S.; Kim, Y-W; Park, Y-J, Phys. Lett. B, 656, 221 (2007) · Zbl 1246.83137 · doi:10.1016/j.physletb.2007.09.056
[35] Banerjee, R.; Majhi, B. R.; Samanta, S., Phys. Rev. D, 77, 124035x (2012) · doi:10.1103/physrevd.77.124035
[36] Banerjee, R.; Majhi, B. R.; Modak, S. K., Class. Quantum Grav., 26 (2009) · Zbl 1163.83345 · doi:10.1088/0264-9381/26/8/085010
[37] Rahaman, F.; Kuhfittig, P. K F.; Chakraborty, K.; Usmani, A. A.; Ray, S., Gen. Relativ. Gravit., 44, 905 (2012) · Zbl 1238.83043 · doi:10.1007/s10714-011-1320-5
[38] Radinschi, I.; Rahaman, F.; Mondal, U. F., Int. J. Theor. Phys., 52, 96 (2013) · Zbl 1263.83105 · doi:10.1007/s10773-012-1304-6
[39] Bao, D.; Shern, S. S.; Chen, Z., An Introduction to Riemann-Finsler Geometry (2000), New York: Springer, New York · Zbl 0954.53001
[40] Pfeifer, C.; Wohlfarth, M.; Bičák, J.; Ledvinka, T., Proceedings in Physics, p 157 (2014), Berlin: Springer, Berlin
[41] Kouretsis, A. P.; Stathakopoulos, M.; Stavrinos, P. C. (2012)
[42] Girelli, F.; Liberati, S.; Sindoni, L., Phys. Rev. D, 75 (2007) · doi:10.1103/physrevd.75.064015
[43] Gibbons, G. W.; Gomis, J.; Pope, C. N., Phys. Rev. D, 76 (2007) · doi:10.1103/physrevd.76.081701
[44] Hohmann, M.; Pfeifer, C., Phys. Rev. D, 95 (2017) · doi:10.1103/physrevd.95.104021
[45] Caponio, E.; Javaloyes, M. Á.; Masiello, A., Math. Ann., 351, 365 (2011) · Zbl 1228.53052 · doi:10.1007/s00208-010-0602-7
[46] Caponio, E.; Javaloyes, M. A.; Sánchez, M., Rev. Mat. Iberoamericana, 27, 919 (2011) · Zbl 1229.53070 · doi:10.4171/rmi/658
[47] Caponio, E.; Javaloyes, M. A.; Masiello, A., J. Phys. A: Math. Theor., 43 (2010) · Zbl 1192.53069 · doi:10.1088/1751-8113/43/13/135207
[48] Vacaru, S. I., J. Math. Phys., 46 (2005) · Zbl 1067.83011 · doi:10.1063/1.1869538
[49] Vacaru, S.; Stavrinos, P.; Gaburov, E.; Gonta, D., Clifford and Riemann- Finsler Structures in Geometric Mechanics and Gravity, Differential Geometry - Dynamical Systems (2006), Geometry Balkan Press · Zbl 1114.53062
[50] Akbar-Zadeh, H., barb, 74, 281 (1988) · Zbl 0686.53020 · doi:10.3406/barb.1988.57782
[51] Li, X.; Chang, Z., Phys. Rev. D, 90 (2014) · doi:10.1103/physrevd.90.064049
[52] Chowdhury, S. R.; Deb, D.; Rahaman, F.; Ray, S.; Guha, B. K., Int. J. Mod. Phys. D, 29, 2050001 (2020) · doi:10.1142/s0218271820500017
[53] Lopez-Dominguez, J. C.; Obregon, O.; Sabido, M.; Ramirez, C., Phys. Rev. D, 74 (2006) · doi:10.1103/physrevd.74.084024
[54] Mukherjee, P.; Saha, A., Phys. Rev. D, 77 (2008) · doi:10.1103/physrevd.77.064014
[55] Chaichian, M.; Tureanu, A.; Zet, G., Phys. Lett. B, 660, 573 (2008) · Zbl 1246.83151 · doi:10.1016/j.physletb.2008.01.029
[56] Balbinot, R.; Barletta, A., Class. Quantum Grav., 6, 195 (1989) · doi:10.1088/0264-9381/6/2/013
[57] Balbinot, R.; Fabbri, A.; Frolov, V.; Nicolini, P.; Sutton, P. J.; Zelnikov, A., Phys. Rev. D, 63 (2001) · doi:10.1103/physrevd.63.084029
[58] Balbinot, R.; Fabbri, A.; Nicolini, P.; Sutton, P. J., Phys. Rev. D, 66 (2002) · doi:10.1103/physrevd.66.024014
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.