【作者】 张云；

【导师】 荆继良；

【作者基本信息】 湖南师范大学 ， 理论物理， 2006， 硕士

【摘要】 利用Newman-Penrose形式,在具有整体单极子的Schwarzshild Anti-de Sitter（Ads）时空和Reisser-Nordstrom（RN）AdS时空中,首先对Dirac场和Rarita-Schwinger（RS）场方程进行了变量分离和退耦合,然后利用Horowitz-Hubeny方法计算了黑洞的似正模,具体结果如下: 对于Dirac场扰动下的渐近AdS时空中的整体单极子黑洞,我们分析了不同真空涨落值（描述整体单极子的参量）下不同半径的黑洞的似正模。得出如下结论: 1.对于大黑洞,似正模的实部与虚部是温度的线性函数。对于中小黑洞,似正模的实部与半径的函数关系比较接近温度与半径的函数关系;而似正模的虚部比较接近半径的线性函数。 2.大黑洞似正模的值与真空涨落值的大小关系不大。中小黑洞则不一样,随着真空涨落值的增加,似正模的实部、虚部与半径的函数关系都逐渐接近于半径的线性函数。 对于RS场扰动下的渐进AdS时空中的RN黑洞。对于大黑洞,我们分别研究了黑洞半径,电荷,扰动场角动量的量子数对黑洞似正模的基频与高阶谐波的影响。得出如下结论: 1.黑洞似正模的实部与虚部是温度的线性函数,但是这种线性函数的斜率与黑洞电荷相关。黑洞电荷越接近极值电荷(Q_ext),线性函数的斜率越大。 2.由于对于不同半径的RN黑洞电荷极值不同,为清楚起见,我们将黑洞半径取定,来寻找似正模与黑洞电荷的关系。我们发现:随着电荷的增加,似正模的实部不是单调变化的,而是先减小后增加;似正模的虚部一直单调减小（绝对值增加）。当电荷接近某一临界值时,会出现一种实部为零的非振荡解,而且电荷越大,非振荡解的绝对值越小。我们所计算的0到4阶谐波都出现了这种情况。 3.在不改变黑洞半径的情况下,我们改变黑洞所带电荷,研究了似更多还原

【Abstract】 By using the Newman-Penrose formalism, the equation of the Dirac and the RS fields are separated and decoupled in the Schwarzschild AdS and the RN AdS spacetimes, and the Quasinormal modes are computed by using Horowitz-Hubeny approach.We study the Dirac QNMs of the schwarzschild-AdS black hole with a global monopole at first. From the result by changing the vacuum expectation, which correlate the global monopole, and the horizon radius of the black hole, we find:1. The relation between the QNMs of large black holes with a global monopole and the Hawking temperature is a linear relation;The relation between the real parts of QNMs of intermediate and small black hole with a global monopole and the Hawking temperature is a linear relation too;But the relation between the imaginary parts of QNMs of intermediate and small black hole with a global monopole and the horizon radius is a linear relation .2. The vacuum expectation little affects the QNMs of large black hole with a global monopole. But it is the different case for intermediate and small black hole with a global monopole. As the vacuum expectation increases, both real parts and imaginary parts of the QNMs approximates to the linear functions of horizon radius.Then, we studied the Rarita-Schwinger(RS) field quasinormal frequencies of Reissner-Nordstrom-anti-de Sitter black hole. And we calculated by changing the horizon radius of large black hole, the charge of black hole, the angular quantum number of RS field. the conclusions are:1. Its QNMs are a linear function of Hawking temperature, but the slope is affected by the charge. As the charge approaches to the extreme charge, the slope increases.2. We wouldn’t change the horizon radius of black hole for which will affect the value of extreme charge. So we take horizon radius of the black hole as r_+ = 100. we find: as the charge increased, the real part of QNMs decreased at first than increased;the imaginary part decreased monotonously. When the charge is closeto a critical value, a non-oscillatory modes appear. And as the charge increased, the absolute values of the non-oscillatory modes decreased. This case at least exists when overtone number less than 4.3. We studied the hight overtone quasinormal frequencies, and find they become evenly spaced for high overtone number n. We changed the charge of black hole in the course of study, and also find the non-oscillatory modes when charge is large.4. We studied the quasinormal frequencies with different I, and find that the quasinormal frequencies depend very weakly on I. But as the increase of the angular quantum number I, The Re(u>) increases (decreases the oscillatory time scale) and \Im(u)\ decreases (increases the damping time scale).更多还原