Taub-NUT黑洞的霍金辐射与反常现象

发布时间：2018-07-26 17:59

【摘要】： 1974年Hawking证明了黑洞并非全“黑”,而是能够从其视界处向外辐射粒子,这也是量子力学和广义相对论相结合的成果,因此研究霍金辐射具有十分重要的意义。至今为止已经有许多计算霍金辐射的方法。其中,霍金的最初解决方案是用到了Bogoliubov变换,解析延拓和几何光学近似。对标量场入射波和出射波的正负频解分别构造了一组正交完备基,相应地定义了两个不等价的真空态,再由Bogoliubov变换求出正负频混合系数。两套不等价真空出现了正负频混模式是产生粒子的关键。近年来,Iso, Robinson和Wilczek等人提出了通过降维技术和消除视界处的反常来计算霍金辐射的新方法,与共形反常方法不同的是他们通过利用了有效场理论在视界处的规范反常和引力反常得到了黑洞的霍金温度以及黑洞的其它一些物理量。此方法由于大大简化了计算过程,且物理意义明确等优越性,得到了广大科研工作者的支持。基于以上研究成果,本文我们主要研究了Taub-NUT黑洞无穷远处的能动张量流和霍金温度。首先我们通过降维技术,也就Damour-Ruffini方法,成功的将Taub-NUT黑洞的四维线元在视界处简化为二维有效度规。这一过程很大程度上简化了复杂的计算过程同时也不失其合理性。然后,再根据视界处附近的反常理论和反常协变有效作用量,从而,在Taub-NUT时空无穷远处,我们得到了Taub-NUT黑洞协变能量动量张量的( r ? t)分量,以及它与霍金温度的关系式。
[Abstract]:In 1974, Hawking proved that a black hole is not a total black hole, but can radiate particles outward from its horizon. This is also the result of the combination of quantum mechanics and general relativity, so the study of Hawking radiation is of great significance. There have been many methods of calculating Hawking radiation so far. Among them, Hawking's initial solution is the use of Bogoliubov transformation, analytic extension and geometric optical approximation. A set of orthogonal complete bases are constructed for the positive and negative frequency solutions of incident wave and output wave in scalar field respectively. Two nonequivalent vacuum states are defined accordingly and the mixing coefficients of positive and negative frequencies are obtained by Bogoliubov transform. The occurrence of positive and negative mixing modes in two sets of unequal vacuum is the key to produce particles. In recent years, Iso, Robinson and Wilczek have proposed a new method to calculate Hawking radiation by reducing dimension and eliminating anomalies at the horizon. Different from the conformal anomaly method, they obtained the Hawking temperature of black hole and some other physical quantities of black hole by using the gauge anomaly and gravitational anomaly of effective field theory at the horizon. This method has been supported by many researchers because it greatly simplifies the calculation process and has the advantages of clear physical meaning. Based on the above results, we study the active Zhang Liang current and Hawking temperature at the infinite distance of the Taub-NUT black hole. First, we successfully simplify the four-dimensional line element of Taub-NUT black hole into a two-dimensional effective metric at the horizon by using the dimensionality reduction technique and the Damour-Ruffini method. This process greatly simplifies the complicated calculation process without losing its rationality. Then, according to the anomalous theory near the horizon and the anomalous covariant effective action, we obtain the (r? t) component of the covariable energy momentum Zhang Liang of Taub-NUT black hole and its relation to Hawking temperature at infinity of Taub-NUT spacetime.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2010
【分类号】：P145.8

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