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In recent years, thermodynamics and phase transitions of black holes in extended phase space have been extensively studied. The results show that the original first law of thermodynamics needs revising and new phase transitions will appear. However, so far, Hawking tunneling radiation has not been widely studied in the extended phase space. In particular, whether the tunneling radiation probability changes at this time is still uncertain. This work focuses on this topic, that is, to calculate the specific value of the tunneling probability in the extended phase space and ascertains whether the results obtained in the normal phase space are consistent with those in the extended phase space. The methods used herein are described below. Taking Reissner-Nordstrom-AdS black holes with global monopole for example, the cosmological parameters are regarded as dynamic variables, which is different from previous treatment methods that regard them as constants and ignore their contributions to the tunneling probability. In particular, cosmological parameters are introduced and regarded as thermodynamic pressure when the tunneling probability is calculated, and their contribution to the tunneling probability is considered. In the work the tunneling process of mass particles is mainly studied. The outgoing particles are viewed as spherical de Broglie waves, and then the relative phase velocity and group velocity are calculated. The geodesic equation is obtained according to the relationship between the two velocities, and the tunneling probability is calculated from the geodesic equation. It is concluded that the results show that the tunneling probability of the ingoing particles is proportional to the difference in the Bekenstein-Hawking entropy of the black hole before and after the particles tunnel, and the radiation spectrum deviates from the pure thermal spectrum, which is exactly the same as the case that the cosmological parameters are treated as constants. This means that the tunneling probability of particles can be obtained in the extended phase space, and the tunneling process does not depend on thermodynamic parameters. In addition, it is found that although the global monopole affects the dynamical behavior and thermodynamic quantity of the particle, it does not affect the entropy change or tunneling rate. In other words, the conclusion that the tunneling probability in extended phase space is exactly the same as that in normal phase space does not depend on the space-time topology.
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Keywords:
- Hawking radiation /
- cosmology parameters /
- thermodynamic pressure /
- global monopole
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[18] Vagenas E C 2002 Phys. Lett. B 533 302Google Scholar
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[25] 韩亦文 2005 物理学报 54 5018Google Scholar
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[26] Han Y W 2005 Chin. Phys. Lett. 22 2769Google Scholar
[27] 张靖仪, 赵峥 2006 物理学报 55 3796Google Scholar
Zhang J Y, Zhao Z 2006 Acta Phys. Sin. 55 3796Google Scholar
[28] Liu W 2006 Phys. Lett. B 634 541Google Scholar
[29] Han Y W 2007 Chin. Phys. 16 0923Google Scholar
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[31] Jiang Q Q, Wu S Q 2006 Phys. Lett. B 635 151Google Scholar
[32] Jiang Q Q, Wu S Q, Cai X 2006 Phys. Rev. D 73 064003Google Scholar
[33] Jiang Q Q, Cai X 2009 JHEP 11 110Google Scholar
[34] Ding C, Wang M, Jing J 2009 Phys. Lett. B 676 99Google Scholar
[35] Zeng X X, Yang S Z 2009 Chin. Phys. B 18 462Google Scholar
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[55] Barriola M, Vilenkin A 1989 Phys. Rev. Lett. 63 341Google Scholar
[56] Yu H W 1994 Nucl. Phys. B 430 427Google Scholar
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[59] 曾晓雄, 胡馨匀, 韩亦文, 刘显明 2015 中国科学: 物理学 力学 天文学 45 080401Google Scholar
Zeng X X, Hu X Y, Han Y W, Liu X M 2015 Sci. China-Phys. Mech. Astron. 45 080401Google Scholar
[60] 周亮, 张靖仪 2010 物理学报 59 4380Google Scholar
Zhou L, Zhang J Y 2010 Acta Phys. Sin. 59 4380Google Scholar
[61] Gao C J, Sen Y G 2002 Chin. Phys. Lett. 19 477Google Scholar
[62] Painlevé P 1921 Comptes Rendus Academie des Sciences (Serie Non Specifiee) 173 677
[63] Gullstrand A 1922 Arkiv. Mat. Astron. Fys. 16 15
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[1] Akiyama K, Alberdi A, Alef W, et al. 2019 Astrophys. J. Lett. 875 L1Google Scholar
[2] Hawking S W 1974 Nature 248 30Google Scholar
[3] Hawking S W 1975 Commun. Math. Phys. 43 199Google Scholar
[4] Christodoulou D 1970 Phys. Rev. Lett. 25 1596Google Scholar
[5] BardeenJ M 1970 Nature 226 64Google Scholar
[6] Bekenstein J D 1973 Phys. Rev. D 7 2333Google Scholar
[7] Damour T, Ruffini R 1976 Phys. Rev. D 14 332Google Scholar
[8] Gibbons G W, Hawking S W 1977 Phys. Rev. D 15 2752Google Scholar
[9] York J W 1986 Phys. Rev. D 33 2091Google Scholar
[10] Whiting B F, York J W 1988 Phys. Rev. Lett. 61 1336Google Scholar
[11] Punsly B 1992 Phys. Rev. D 46 1288Google Scholar
[12] Srinivasan K, Padmanabhan T 1999 Phys. Rev. D 60 024007Google Scholar
[13] Robinson S P, Wilczek F 2005 Phys. Rev. Lett. 95 011303Google Scholar
[14] Han Y W, Zhang J Y 2010 Phys. Lett. B 692 74Google Scholar
[15] Han Y W, Chen G 2012 Phys. Lett. B 714 127Google Scholar
[16] ParikhM K, Wilczek F 2000 Phys. Rev. Lett. 85 5042Google Scholar
[17] Hemming S, Keski-Vakkuri E 2001 Phys. Rev. D 64 044006Google Scholar
[18] Vagenas E C 2002 Phys. Lett. B 533 302Google Scholar
[19] Medved A J M 2002 Phys. Rev. D 66 124009Google Scholar
[20] Setare M R, Vagenas E C 2004 Phys. Lett. B 584 127Google Scholar
[21] Parikh M 2004 Int. J. Mod. Phys. D 13 2351Google Scholar
[22] Zhang J, Zhao Z 2005 Nucl. Phys. B 725 173Google Scholar
[23] Medved A J M, Vagenas E C 2005 Mod. Phys. Lett. A 20 2449Google Scholar
[24] Zhang J, Zhao Z 2011 Phys. Rev. D 83 064028Google Scholar
[25] 韩亦文 2005 物理学报 54 5018Google Scholar
Han Y W 2005 Acta Phys. Sin. 54 5018Google Scholar
[26] Han Y W 2005 Chin. Phys. Lett. 22 2769Google Scholar
[27] 张靖仪, 赵峥 2006 物理学报 55 3796Google Scholar
Zhang J Y, Zhao Z 2006 Acta Phys. Sin. 55 3796Google Scholar
[28] Liu W 2006 Phys. Lett. B 634 541Google Scholar
[29] Han Y W 2007 Chin. Phys. 16 0923Google Scholar
[30] HanY W, Yang S Z 2007 Commun. Theor. Phys. 47 1145Google Scholar
[31] Jiang Q Q, Wu S Q 2006 Phys. Lett. B 635 151Google Scholar
[32] Jiang Q Q, Wu S Q, Cai X 2006 Phys. Rev. D 73 064003Google Scholar
[33] Jiang Q Q, Cai X 2009 JHEP 11 110Google Scholar
[34] Ding C, Wang M, Jing J 2009 Phys. Lett. B 676 99Google Scholar
[35] Zeng X X, Yang S Z 2009 Chin. Phys. B 18 462Google Scholar
[36] Christina S, Singh T I 2021 Gen Relativ Gravit 53 43Google Scholar
[37] Vishnulal C, Basak S, Das S 2021 Phys. Rev. D 104 104011Google Scholar
[38] Cai R G, Cao L M, Li L, Yang R Q 2013 JHEP2013 5Google Scholar
[39] Johnson C V 2014 Class. Quant. Grav. 31 205002Google Scholar
[40] Caceres E, Nguyen P H, Pedraza J F 2015 JHEP 2015 184Google Scholar
[41] Mandal A, Samanta S, Majhi B R 2016 Phys. Rev. D 94 064069Google Scholar
[42] Caldarelli M M, Cognola G, Klemm D 2000 Class. Quantum Grav. 17 399Google Scholar
[43] Hendi S H, Panahiyan S, EslamPanah B, Momennia M 2016 Ann. Phys. (Berlin) 528 819Google Scholar
[44] Kastor D, Ray S, Traschen J 2009 Class. Quant. Grav. 26 195011Google Scholar
[45] Kubizňák D, Mann R B 2012 JHEP 2012 33Google Scholar
[46] DolanB P 2011 Class. Quant. Grav. 28 125020Google Scholar
[47] Cvetič M, Gibbons G W, Kubizňák D 2011 Phys. Rev. D 84 024037Google Scholar
[48] Altamirano N, Kubizňák D, Mann R B 2013 Phys. Rev. D 88 101502Google Scholar
[49] Dolan B P, Kostouki A, Kubizňák D 2014 Class. Quant. Grav. 31 242001Google Scholar
[50] Hennigar R A, Mann R B, Tjoa E 2017 Phys. Rev. Lett. 118 021301Google Scholar
[51] Wei S W, Liu Y X, Mann R B 2019 Phys. Rev. Lett. 123 071103Google Scholar
[52] Zeng X X, Han Y W, Che D Y 2019 Chin. Phys. C 43 105104Google Scholar
[53] Han Y W, Zeng X X, Hong Y 2019 Eur. Phys. J. C 79 252Google Scholar
[54] Ren Z X, Zeng X X, Han Y W, Hu C 2023 Nucl. Phys. B 990 116153Google Scholar
[55] Barriola M, Vilenkin A 1989 Phys. Rev. Lett. 63 341Google Scholar
[56] Yu H W 1994 Nucl. Phys. B 430 427Google Scholar
[57] He A, Tao J, Wang P, Xue Y, Zhang L 2022 Eur. Phys. J. C 82 683Google Scholar
[58] Chen S, Wang L, Ding C, et al. 2010 Nucl. Phys. B 836 222Google Scholar
[59] 曾晓雄, 胡馨匀, 韩亦文, 刘显明 2015 中国科学: 物理学 力学 天文学 45 080401Google Scholar
Zeng X X, Hu X Y, Han Y W, Liu X M 2015 Sci. China-Phys. Mech. Astron. 45 080401Google Scholar
[60] 周亮, 张靖仪 2010 物理学报 59 4380Google Scholar
Zhou L, Zhang J Y 2010 Acta Phys. Sin. 59 4380Google Scholar
[61] Gao C J, Sen Y G 2002 Chin. Phys. Lett. 19 477Google Scholar
[62] Painlevé P 1921 Comptes Rendus Academie des Sciences (Serie Non Specifiee) 173 677
[63] Gullstrand A 1922 Arkiv. Mat. Astron. Fys. 16 15
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