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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= 2 M( 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.
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关键词:
- 修正Dirac方程/
- 霍金辐射/
- Hamilton-Jacobi方程/
- 黑洞热力学
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 aaffects the mass term of the Dirac field, and the aether-like term containing the parameter cmodifies the coefficient term of the action Sof 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= 2 M( 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 ccan 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:
- modified Dirac field equation/
- Hawking radiation/
- Hamilton-Jacobi equation/
- black hole thermodynamics
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