渐近安全引力中黑洞的拟正则模

发布时间：2018-06-01 15:38

本文选题：渐近安全引力 + 黑洞的拟正则模　；参考：《上海师范大学》2012年硕士论文

【摘要】：渐近安全引力将经典引力理论看作是某种量子场论的有效理论,它是一种有希望的量子引力理论.在渐近安全引力的图像中,静态球对称黑洞度规要受到量子效应的修正.这种量子修正在黑洞质量较小时非常显著,而对天体质量黑洞,这种量子修正的效应非常小.拟正则模是黑洞在外界微扰下的本征振动模式,它由复数频率表征.复频率的实部刻画振动的频率,虚部表示振动的衰减率.计算黑洞的拟正则模对考察黑洞对线性微扰的稳定性有关键的作用,如果黑洞拟正则模的虚部为负,则表明在线性微扰下,黑洞是稳定的. 本文研究了有量子修正的静态球对称黑洞的拟正则模,并考察了量子修正黑洞的稳定性.我们首先使用珀施尔特勒势的近似方法考察了在角量子数趋于极限时,量子效应对黑洞拟正则的影响.随后又使用三阶WKB法和连分数法分别计算了量子修正黑洞的拟正则模.这两种不同方法的计算结果吻合的相当好,并与我们使用珀施尔特勒势法所做近似分析得到的结果一致.我们发现随着量子修正效应的增大,拟正则模的实部变大,而虚部的绝对值变小.这表明随着量子修正效应的增加,黑洞的振动频率变快,振幅的衰减率变慢.我们最后使用有限元积分的方法模拟了量子修正黑洞的标量扰动,结果与我们前面数值计算的结果一致.我们发现尽管量子效应造成拟正模变化,但它并不影响黑洞的稳定性,这表明考虑了渐近安全引力的量子修正后,在线性微扰下微观黑洞依然是稳定的.
[Abstract]:Asymptotically safe gravitation regards the classical gravitational theory as an effective theory of some quantum field theory, which is a promising quantum gravitational theory. In an image of asymptotically safe gravity, the static spherically symmetric black hole metric is modified by quantum effects. The quantum correction is very significant when the mass of the black hole is small, but the effect of the quantum correction on the celestial mass black hole is very small. Quasi regular mode is the intrinsic vibration mode of black hole under external perturbation, which is characterized by complex frequency. The real part of complex frequency depicts the frequency of vibration, and the imaginary part represents the attenuation rate of vibration. The calculation of the quasi-regular modes of a black hole plays a key role in investigating the stability of a black hole to a linear perturbation. If the imaginary part of the quasi-regular mode of a black hole is negative, it is shown that the black hole is stable under the linear perturbation. In this paper, the quasi-regular modes of a static spherically symmetric black hole with a quantum correction are studied, and the stability of a quantum modified black hole is investigated. We first investigate the effect of quantum effects on the quasi-regularity of black holes when angular quantum numbers tend to be limited by using the approximate method of Perschltler potential. Then the quasi regular modes of a quantum modified black hole are calculated by using the third order WKB method and the continued fraction method respectively. The calculated results of these two different methods are in good agreement with the approximate results obtained by using the Perschltler potential method. We find that with the increase of the quantum correction effect, the real part of the quasi-regular module becomes larger, while the absolute value of the imaginary part becomes smaller. This indicates that with the increase of quantum correction effect, the vibration frequency of black hole becomes faster and the attenuation rate of amplitude becomes slower. Finally, we simulate the scalar perturbation of the quantum modified black hole by using the finite element integral method, and the results are in agreement with our previous numerical results. We find that the quasi-positive mode change caused by quantum effect does not affect the stability of the black hole, which indicates that the microscopic black hole is stable under linear perturbation after the quantum correction of asymptotically safe gravity is taken into account.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：P145.8

【共引文献】