洛伦兹破缺理论与Vaidya黑洞弯曲时空中的Dirac粒子隧穿辐射特征

蒲瑾; 杨树政; 林恺

doi:10.7498/aps.68.20190437

摘要

本文把平直时空中的洛伦兹对称性破缺的Dirac方程推广到动态Vaidya黑洞弯曲时空中. 由于动态Vaidya黑洞的表观视界与类时极限面重合, 根据霍金辐射量子效应理论, 我们在Vaidya黑洞的表观视界r_a = 2M(v)处研究了洛伦兹破缺理论对Dirac粒子Hawking隧穿辐射特征的影响. 我们通过gamma矩阵的对易性质和半经典近似得到了一个新的洛伦兹对称性破缺的Dirac-Hamilton-Jacobi方程, 并利用这一修正的Dirac-Hamilton-Jacobi方程研究了Dirac粒子隧穿辐射的特征, 讨论了洛伦兹对称性破缺对动态球对称Vaidya黑洞的热力学参数的影响. 结果发现, 洛伦兹破缺理论中仅有类以太修正项会对黑洞热力学性质带来修正. 同时, 还发现修正Hawking温度与类以太矢量修正项系数的正负有关, 而我们之前应用洛伦兹破缺理论研究标量粒子的修正Hawking温度也是与类以太矢量修正项系数的正负有关的.

关键词:

Abstract

In this paper, the modified Hawking radiation for Dirac particles via tunneling from the apparent horizon of Vaidya black hole is studied by using the Lorentz-violating Dirac field theory. We first extend the gamma matric from flat spacetime to the curved spacetime in the Lorentz-violating Dirac field theory, and generalize the general derivative to the covariant derivative. Then, by considering the commutative relation of the gamma matric, the Dirac equation in the Lorentz-violating Dirac field theory is obtained, which contains three correction terms related to the Lorentz-symmetry violation. In the semiclassical approximation, the modified Hamilton-Jacobi equation is obtained by using the commutative relation of gamma matric and treating the aether-like vector in the Lorentz-violating theory as a constant. We find that the modified Hamilton-Jacobi equation contains only two correction terms based on the Lorentz-symmetry violation, i.e. the corrected term containing the parameter a affects the mass term of the Dirac field, and the aether-like term containing the parameter c modifies the coefficient term of the action S of the separating variable. According to the modified Hamilton-Jacobi equation, we study the effect of Lorentz-symmetry violation on the characteristics of Hawking radiation for Dirac particles via tunneling from the apparent horizon r_a = 2M(v) of Vaidya black hole (the apparent horizon of Vaidya black hole coincides with the timelike limit surface, so the apparent horizon can be regarded as the boundary of Vaidya black hole). Since the Hawking tunneling radiation of black holes is the radial property at the horizon of black holes, we finally find that only the aether-like term containing the parameter c can modify the characteristics of Dirac particles’ tunneling radiation from the black hole. In addition, the corrected Hawking temperature of the black hole caused by considering the effect on the Lorentz-violating Dirac field theory has a small correction related to the aether-like term, which is consistent with the results obtained by studying the characteristics of Hawking tunneling radiation for scalar particles in the Lorentz-violating scalar field theory. The results suggest that the Lorentz-symmetry violation theory may provide a new method to further study the information loss paradox of black holes.

Keywords:

作者及机构信息

1.
西华师范大学物理与空间科学学院, 南充　637002

2.
电子科技大学物理学院, 成都　610054

3.
中国地质大学(武汉)地球物理与空间信息学院, 地球内部多尺度成像湖北省重点实验室, 武汉　430074

4.
Escola de Engenharia de Lorena, Universidade de Sao Paulo, 12602-810, Lorena, Sao Paulo, Brazil

通信作者: 杨树政, szyangphys@126.com

基金项目: 国家自然科学基金(批准号: 11573022, 11805166)和西华师范大学英才科研基金(批准号: 17YC513, 17C050)

Authors and contacts

1.
College of Physics and Space Science, China West Normal University, Nanchong 637002, China

2.
School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China

3.
Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics,China University of Geosciences, Wuhan 430074, China

4.
Escola de Engenharia de Lorena, Universidade de Sao Paulo, 12602-810, Lorena, Sao Paulo, Brazil

Corresponding author: Yang Shu-Zheng, szyangphys@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11573022, 11805166) and the Starting Funds of China West Normal University, China (Grant Nos. 17YC513, 17C050)

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参考文献

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施引文献

[1]	Horava P 2009 Phys. Rev. D 79 084008 Google Scholar
[2]	Jacobson T, Mattingly D 2001 Phys. Rev. D 64 024028 Google Scholar
[3]	Lin K, Mukohyama K, Wang A, Zhu T 2014 Phys. Rev. D 89 084022 Google Scholar
[4]	Mukohyama S 2010 Class. Quant. Grav. 27 223101 Google Scholar
[5]	Kostelecky V A, Samuel S 1989 Phys. Rev. Lett. 63 224 Google Scholar
[6]	Jackiw R, Kostelecky V A 1999 Phys. Rev. Lett. 82 3572 Google Scholar
[7]	Colladay D, McDonald P 2007 Phys. Rev. D 75 105002 Google Scholar
[8]	Nascimento J R, Petrov A Yu, Reyes C M 2015 Phys. Rev. D 92 045030 Google Scholar
[9]	Casana R, Ferreira M M, Jr, Moreira R P M 2011 Phys. Rev. D 84 125014 Google Scholar
[10]	Hawking S W 1974 Nature 248 30 Google Scholar
[11]	Hawking S W 1975 Commun. Math. Phys. 43 199 Google Scholar
[12]	Robinson S P, Wilczek F 2005 Phys. Rev. Lett. 95 011303 Google Scholar
[13]	Damoar T, Ruffini R 1976 Phys. Rev. D 14 332 Google Scholar
[14]	Sannan S 1988 Gen. Relativ. Gravit. 20 239 Google Scholar
[15]	Kraus P, Wilczek F 1995 Nucl. Phys. B 433 403 Google Scholar
[16]	Parikh M K, Wilczek F 2000 Phys. Rev. Lett. 85 5042 Google Scholar
[17]	Hemming S, Keski-Vakkuri E 2001 Phys. Rev. D 64 044006 Google Scholar
[18]	Jiang Q Q, Wu S Q, Cai X 2007 Phys. Rev. D 75 064029 Google Scholar
[19]	Iso S, Umetsu H, Wilczek F 2006 Phys. Rev. D 74 044017 Google Scholar
[20]	Medved A J M 2002 Phys. Rev. D 66 124009 Google Scholar
[21]	Parikh M K 2006 The Tenth Marcel Grossmann Meeting Rio de Janeiro, Brazil, February, 2006 pp1585-1590 [arXiv: hep-th/0402166]
[22]	Zhang J Y, Zhao Z 2006 Phys. Lett. B 638 110 Google Scholar
[23]	Akhmedov E T, Akhmedova V, Singleton D 2006 Phys. Lett. B 642 124 Google Scholar
[24]	Srinivasan K, Padmanabhan T 1999 Phys. Rev. D 60 24007 Google Scholar
[25]	Shankaranarayanan S, Padmanabhan T, Srinivasan K 2002 Class. Quantum Grav. 19 2671 Google Scholar
[26]	Kerner R, Mann R B 2008 Class. Quantum Grav. 25 095014 Google Scholar
[27]	Kerner R, Mann R B 2008 Phys. Lett. B 665 277 Google Scholar
[28]	Li R, Ren J R, Wei S W 2008 Class. Quantum Grav. 25 125016 Google Scholar
[29]	Chen D Y, Jiang Q Q, Zu X T 2008 Class. Quantum Grav. 25 205022 Google Scholar
[30]	Criscienzo R D, Vanzo L 2008 Europhys. Lett. 82 60001 Google Scholar
[31]	Li H L, Yang S Z, Zhou T J, Lin R 2008 Europhys. Lett. 84 20003 Google Scholar
[32]	Jiang Q Q 2008 Phys. Lett. B 666 517 Google Scholar
[33]	Lin K, Yang S Z 2009 Int. J. Theor. Phys. 48 2061 Google Scholar
[34]	Lin K, Yang S Z 2009 Phys. Rev. D 79 064035 Google Scholar
[35]	Lin K, Yang S Z 2009 Phys. Lett. B 674 127 Google Scholar
[36]	Lin K, Yang S Z 2011 Chin. Phys. B 20 110403 Google Scholar
[37]	Yang S Z, Lin K 2019 Acta Phys. Sin. 68 060401
[38]	Criscienzo R D, Nadalini M, Vanzo L, Zernini S, Zoccatelli G 2007 Phys. Lett. B 657 107 Google Scholar
[39]	Hayward S A 1998 Class. Quantum Grav. 15 3147 Google Scholar
[40]	Kim S W 2014 Crav. & Cosm. 20 247
[41]	Kodama H 1980 Prog. Theor. Phys. 63 1217 Google Scholar

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