【作者】 毛普健；

【导师】 任继荣；

【作者基本信息】 兰州大学 ， 理论物理， 2012， 硕士

【摘要】 本文基于量子反常抵消方法,有效作用量方法,Damour-Ruffini-Sannan(DRS)方法以及密度矩阵技术研究了五维Godel黑洞和五维Myers-Perry黑洞Dirac粒子的Hawking辐射和Hawking黑体谱。利用维度约化技术,我们发现五维Godel黑洞和五维Myers-Perry黑洞中的费米场可以由(1+1)维背景时空下的二分量量子场和Dilaton场与U(1)规范场的耦合所描述。在这个有效两维的量子场中,因为所有入的模式不能影响到视界面外部的物理效应,在规范和一般坐标对称性条件下,外部的有效二维作用量体现出了奇异性。为了抵消奇异反常,Hawking通量就变成了视界面上的反常荷。从而得到了Hawking温度和Hawking通量。在有效作用量基础上,通过取协变的边界条件,协变的规范通流以及协变能动张量,由迹反常也可以正确的推导出Hawking通量。这种方法非常的直接和有效,因为通量和能动张量的表达可直接通过对有效作用量的函数微分获得。为了形成对照,我们还通过DRS方法计算了黑洞的Hawking温度。而这三种方法所得到的Hawking温度都和表面引力机制相一致。量子反常抵消取消方法和有效作用量方法所得到的Hawking通量也和Planck分布一致。最后,我们通过密度矩阵技术得到了五维Godel黑洞和五维Myers-Perry黑洞的Hawking辐射谱。结果表明,辐射光谱在Hawking温度下是一个完美的黑体辐射谱。更多还原

【Abstract】 In this thesis, we apply the quantum anomaly cancellation method andthe effective action approach as well as the method ofDamour-Ruffini-Sannan(DRS) to derive Hawking radiation of Dirac particles from five dimensional Godel and Myers-Perry black hole. We also investigate the Hawking black body spectrum of these black holes by using density matrix techniques.Using the dimensional reduction technique, we find that the fermionic field in the back-ground of the Godel and Myers-Perry black hole can be treated as an infinite collection of quantum fields in (1+1)-dimensional background coupled with the dilaton field and the U(1) gauge field near the horizon. In this two-dimensional reduction, as all the ingoing modes can not classically affect physics outside the horizon, the two-dimensional effective action in the exterior region becomes anomalous with respect to gauge or general coordinate symmetries. To cancel the anomaly, the Hawking flux is universally determined only by the value of anomalies at the horizon. Thus Hawking temperature and fluxes are found.Another method to correctly reproduce Hawking fluxes is based on the effective action which is induced from trace anomaly by using the covariant boundary condition and the co-variant gauge current as well as the covariant energy-momentum tensor. This approach is particularly direct and useful since one is able to obtain an expression for the currents and energy-momentum tensors directly by taking appropriate functional derivatives of the effective action.By comparison, we also calculate the Hawking temperature via the method of Damour-Ruffini-Sannan. The Hawking temperature obtained agrees with the surface gravity formula while the Hawking fluxes derived from the anomaly cancellation method and the effective ac-tion approach are in complete agreement with the ones obtained from integrating the Planck distribution. Finally, using density matrix techniques, we obtain the Hawking radiation spectrum of the Godel and Myers-Perry black hole. It is shown that the radiation spectrum is consistent with a perfect blackbody spectrum in the Hawking temperature.更多还原