Einstein-Bumblebee引力理论中的Kerr-Sen-like黑洞玻色子隧穿辐射

谭霞; 杨树政

doi:10.7498/aps.73.20231463

摘要

Lorentz-breaking理论不仅对弯曲时空背景有影响, 而且对于在弯曲时空中的玻色子和费米子的动力学方程都有一定的修正. 因此, 我们需要在不同的黑洞时空中对玻色子和费米子的量子隧穿辐射进行适当的修正. 从而得到经过Lorentz-breaking理论修正后的黑洞Hawking温度等物理量的新表达式及其物理意义. 本文根据Einstein-Bumblebee引力理论中得到的Kerr-Sen-like (KSL)黑洞时空度规, 在标量场作用量中引入aether-like场矢量修正项和弯曲时空中的d’Alembert算符并应用弯曲时空中的变分原理, 研究了此时空度规中的Lorentz-breaking修正项及KSL时空中自旋为零的含有Lorentz-breaking修正项的玻色子动力学方程的新形式. 通过正确选择与KSL时空度规相对应的aether-like场矢量, 求解修正的玻色子动力学方程, 得到了修正的量子隧穿率, 并在此基础上研究了含有Lorentz-breaking修正项的此黑洞的Hawking温度和Bekenstein-Hawking熵. 此外, 还研究了Lorentz-breaking效应对玻色子正、负能级分布及其能级交错的最大值的影响, 从而得出此黑洞时空中的量子非热辐射的条件. 最后对所得到的一系列结果的物理意义进行了深入的讨论.

关键词:

Abstract

Lorentz-breaking theory not only affects the curved space-time background, but also corrects the dynamic equations of bosons and fermions in curved space-time to some extent. Therefore, we need to make appropriate corrections to the quantum tunneling radiation of bosons and fermions in different black hole spacetimes. New expressions of black hole Hawking temperature and other physical quantities modified by Lorentz-breaking theory and their physical meanings are obtained. According to the Kerr-Sen-like (KSL) black hole spacetime metric obtained from Einstein-Bumblebee gravitational theory, by introducing the correction term of the aether-like field vector into the scalar field action and the d’Alembert operator in curved spacetime, and applying the variational principle to curved spacetime, the Lorentz-breaking correction term in the spacetime metric and the new form of the dynamic equation of the bosons with zero spin in KSL spacetime are studied. By correctly selecting the aether-like field vector corresponding to the KSL spacetime metric and solving the modified bosons dynamic equation, the modified quantum tunneling rate is obtained. On this basis, the Hawking temperature and the Bekenstein-Hawking entropy of the black hole with Lorentz-breaking correction term are studied. The effects of Lorentz-breaking theory on the distribution of positive and negative energy levels of bosons and the maximum crossing of energy levels are also studied, and then the condition of quantum non-thermal radiation in the black hole space-time is studied. Finally, the physical significance of a series of results obtained in this work is discussed in depth. The results show that the modified form of the bosons dynamic equation in curved spacetime, with Lorentz-breaking theory taken into account, is shown in Eqs. (26) and (27). The new expressions of the quantum tunneling rate, Bekenstein-Hawking entropy, Hawking temperature and quantum non-thermal radiation energy range of KSL black hole are obtained by applying Eq. (26) to KSL black hole space-time. These results are useful for studying the quantum tunneling radiation characteristics of black holes. It should be noted that the above research results are obtained under the WKB theory and in the semiclassical case. If the effects of different powers of Planck are considered, the above research methods and related results need to be used for conducting further modified research by using the transcendental semi-classical theory.

Keywords:

Lorentz-breaking /
Einstein-Bumblebee gravitational theory /
Kerr-Sen-like black hole /
Bekenstein-Hawking entropy

作者及机构信息

谭霞¹,
杨树政²

1.
齐鲁师范学院物理与电子工程学院, 济南　250200

2.
西华师范大学物理与天文学院, 南充　637002

通信作者: 谭霞, 20152329@qlnu.edu.cn ; 杨树政, szyangphys@126.com

基金项目: 国家自然科学基金(批准号: 12373109)资助的课题.

Authors and contacts

Tan Xia¹,
Yang Shu-Zheng²

1.
College of Physics and Electronic Engineering, Qilu Normal University, Jinan 250200, China

2.
College of Physics and Space Science, China West Normal University, Nanchong 637002, China

Corresponding author: Tan Xia, 20152329@qlnu.edu.cn ; Yang Shu-Zheng, szyangphys@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12373109).

文章全文 : translate this paragraph

参考文献

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施引文献

[1]	Carroll M S, Field G B, Jackiw R 1990 Phys. Rev. D 41 1231 Google Scholar
[2]	Jackiw R, Kostelecky V A 1999 Phys. Rev. Lett. 82 3572 Google Scholar
[3]	Coleman S, Glashow S L 1999 Phys. Rev. D 59 116008 Google Scholar
[4]	Kruglov S I 2012 Phys. Lett. B 718 228 Google Scholar
[5]	Amelino-Camelia G, Ahluwalia D V 2002 Int. J. Mod. Phys. D 11 35 Google Scholar
[6]	Amelino-Camelia G 2004 New J. Phys. 6 188 Google Scholar
[7]	Magueijo J, Smolin L 2002 Phys. Rev. Lett 88 190403 Google Scholar
[8]	Magueijo J, Smolin L 2003 Phys. Rev. D 67 044017 Google Scholar
[9]	Ellis J, Mavromatos N E, Nenopoulos D V 1992 Phys. Lett. B 293 37 Google Scholar
[10]	Ellis J, Mavromatos N E, Nenopoulos D V 1999 Chaos Solitons Fractals 10 345 Google Scholar
[11]	Ellis J R, Mavromatos N E, Sakharov A S 2004 Astropart. Phys. 20 669 Google Scholar
[12]	Kruglov S I 2013 Mod. Phys. Lett. A 28 1350014 Google Scholar
[13]	Jacobson T, Liberati S, Mattingly D 2003 Nature 424 1019 Google Scholar
[14]	Yang S Z, Lin K, Li J, Jiang Q Q 2016 Adv. High Energy Phys. 2016 7058764 Google Scholar
[15]	杨树政, 林恺 2019 物理学报 68 060401 Google Scholar Yang S Z, Lin K 2019 Acta Phys. Sin. 68 060401 Google Scholar
[16]	Yang S Z, Lin K 2019 Sci. Sin-Phys Mech. Astron. 49 019503 Google Scholar
[17]	Li R, Yu Z H, Yang S Z 2023 EPL 141 50001 Google Scholar
[18]	Li R, Ding Q T, Yang S Z 2022 EPL 138 60001 Google Scholar
[19]	Tan X, Liu Y Z, Liu Z E, Sha B, Zhang J, Yang S Z 2020 Mod. Phys. Lett. A 35 2050168 Google Scholar
[20]	Zhang J, Liu Z E, Sha B, Tan X, Liu Y Z, Yang S Z 2020 Adv. High Energy Phys. 2020 2742091 Google Scholar
[21]	Sha B, Liu Z E, Liu Y Z, Tan X, Zhang J, Yang S Z 2020 Chin. Phys. C 44 125104 Google Scholar
[22]	Liu Z E, Tan X, Liu Y Z, Sha B, Zhang J, Yang S Z 2021 Can. J. Phys. 99 451 Google Scholar
[23]	Liu Y Z, Sha B, Tan X, Liu Z, Liu J 2020 Can. J. Phys. 98 999 Google Scholar
[24]	Gomes M, Nascimento J R, Petrov A Y, da Silva A J 2010 Phys. Rev. D 81 045018 Google Scholar
[25]	Mariz T, Nasimento J R, Petrov A Y, Serafim W 2014 Phys. Rev. D 90 045015 Google Scholar
[26]	Casano R, Ferreira M M, Maluf R, dos Santos E P 2013 Phys. Lett. B 726 815 Google Scholar
[27]	Klinkhammer F R, Schreck M 2011 Nucl. Phys. B 848 90 Google Scholar
[28]	Klinkhammer F R, Schreck M 2012 Nucl. Phys. B 856 666 Google Scholar
[29]	Brito F A, Nascimento J R, Passos E, et al. 2007 JHEP 2007 6 Google Scholar
[30]	Li R, Yu Z H, Yang S Z 2022 EPL 139 59001 Google Scholar
[31]	Sohan Kumar Jha, Anisur Rahaman 2021 Eur. Phys. J C 81 345 Google Scholar
[32]	Carleo A, Lambiase G, Mastrototaro L 2022 Eur. Phys. J. C 82 776 Google Scholar
[33]	Yang S Z, Zhao Z 1996 Int. J. Theor. Phys. 35 2455 Google Scholar
[34]	Polarski David, Starobinsky A A 1994 Phys. Rev. D 50 6123 Google Scholar
[35]	Unruh W G 1974 Phys. Rev. D 10 3194 Google Scholar
[36]	Kraus P, Wilczek F 1995 Nucl. Phys. B 433 403 Google Scholar
[37]	Parikh M K, Wilczek F 2000 Phys. Rev. Lett. 85 5042 Google Scholar

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