黑洞熵与黑洞似正规模的研究
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摘要
黑洞熵和黑洞似正规模一直是黑洞物理研究中的两个前沿热门课题。在黑洞熵的研究中,其统计力学起源问题尤为重要,但却一直是困扰理论物理学者的一大难题。因此,对黑洞熵统计起源问题的深入研究将对黑洞物理学乃至量子引力理论的发展起到重要的推动作用。另外,黑洞似正规模与外场的初始扰动无关,而是由黑洞自身的参数决定。这一特点说明,黑洞作为一种天体,它有自己的“特征声音”,而似正规模正是这种“声音”的物理表述。当不久的将来引力波被探测到时,黑洞似正规模可能会成为黑洞存在的直接证据。
本论文包括如下五部分内容：
在第一章中,首先简单回顾了黑洞及其热力学性质,接着,介绍了黑洞熵和黑洞似正规模的定义、研究方法以及意义。
在第二章中,首先应用薄膜模型方法计算了带电dilaton-axion黑洞在渐进平直和渐进非平直两种时空背景下的熵。通过计算视界面附近一薄层内量子场的熵来得到黑洞熵。计算过程中,虽然克服了原始砖墙模型中的部分不完美之处,但仍然需要人为的引入截断因子来消除视界面上的奇异。当把广义测不准原理引入到了薄膜模型中计算黑洞熵时,在无需引入任何截断因子的情形下,视界面附近量子场的发散问题就能够被消除,并且小质量近似问题也能够很好的得以解决。然后,利用留数定理对黑洞熵的积分表达式进行计算,便能够得到与视界面积成正比的黑洞熵。
在第三章中,采用三阶WKB近似方法,分别计算了静态球对称quintessence物质包围的整体单极子黑洞的有质量标量场和无质量Dirac场的低频似正规模,并且详细讨论了似正规模频率与各种参数因子之间的变化关系。
在第四章中,计算了在变形Horava-Lifshitz引力中的静态球对称黑洞的无质量Dirac场的低频似正规模,并且讨论了Horava-Lifshitz参数因子对似正规模的影响。
最后是本论文的结论部分。
The black hole entropy and the quasinormal modes of black holes have long been the important and exciting themes in the black hole physics. The statistical explanation of the black hole entropy is one of the most important aspects, and has long been a puzzled problem to many theoretical physicists, therefore, the investigation on this topic will play an improving role in the black hole physics and even quantum gravitation theory. While, it is well known that the complex frequencies of quasinormal modes are independent of the initial perturbation and just decided by parameters of black hole themselves. In a sense, the quasinormal modes can be regarded as a characteristics sound of black holes. It is widely believed direct way to identify the existence of a black hole, when gravitational wave will be detected in the near future.
The thesis consists of five parts, and is organized as follows:
In Sec.1, a brief introduction of black hole's thermodynamic characters are given at first. Then, the definition, calculation method and motivations of study of the black hole entropy and quasinormal modes are introduced, respectively.
In Sec.2. firstly, the entropy of the charged dilaton-axion black hole is calculated for both asymptotically flat and non-flat cases, using the thin-film model. The thin-film model designates that the black hole entropy is contributed of quantum field by a thin film near the black hole horizon, and the results obtained confirm the Bekenstein-Hawking area-entropy formula. The thin-film model method avoids some drawbacks in the original brick-wall method, but the arbitrary cutoff to remove the divergence near the horizon cannot be avoided yet. For this, the entropy of black holes are corrected to leading order in the Planck length, with the newly modified equation of states density motivated by the generalized uncertainty principle, in the regime of the thin-film model method, which drastically solves the ultraviolet divergences of the just vicinity near the horizon replacing the conventional brick-wall method cutoff with the minimal length. Then, the integral equation of entropy can be solved with residue theorem, which is proportional to the black hole horizon area.
In Sec.3, adopting three-order WKB approximation method, the quasinormal modes of a black hole with a global monopole surrounded by static spherically-symmetric quintessence matter are calculated, for massive scalar fields and massless Dirac fields perturbation, re-spectively, and the influence of different parameters on quasinormal modes frequency are discussed.
In Sec.4, in the deformed Horava-Lifshitz gravity, the black hole quasinormal modes of the massless Dirac field perturbation are calculated, and then the influence of Horava-Lifshitz parameter on quasinormal modes frequency are discussed.
A conclusion is presented in the last section.
本论文包括如下五部分内容：
在第一章中,首先简单回顾了黑洞及其热力学性质,接着,介绍了黑洞熵和黑洞似正规模的定义、研究方法以及意义。
在第二章中,首先应用薄膜模型方法计算了带电dilaton-axion黑洞在渐进平直和渐进非平直两种时空背景下的熵。通过计算视界面附近一薄层内量子场的熵来得到黑洞熵。计算过程中,虽然克服了原始砖墙模型中的部分不完美之处,但仍然需要人为的引入截断因子来消除视界面上的奇异。当把广义测不准原理引入到了薄膜模型中计算黑洞熵时,在无需引入任何截断因子的情形下,视界面附近量子场的发散问题就能够被消除,并且小质量近似问题也能够很好的得以解决。然后,利用留数定理对黑洞熵的积分表达式进行计算,便能够得到与视界面积成正比的黑洞熵。
在第三章中,采用三阶WKB近似方法,分别计算了静态球对称quintessence物质包围的整体单极子黑洞的有质量标量场和无质量Dirac场的低频似正规模,并且详细讨论了似正规模频率与各种参数因子之间的变化关系。
在第四章中,计算了在变形Horava-Lifshitz引力中的静态球对称黑洞的无质量Dirac场的低频似正规模,并且讨论了Horava-Lifshitz参数因子对似正规模的影响。
最后是本论文的结论部分。
The black hole entropy and the quasinormal modes of black holes have long been the important and exciting themes in the black hole physics. The statistical explanation of the black hole entropy is one of the most important aspects, and has long been a puzzled problem to many theoretical physicists, therefore, the investigation on this topic will play an improving role in the black hole physics and even quantum gravitation theory. While, it is well known that the complex frequencies of quasinormal modes are independent of the initial perturbation and just decided by parameters of black hole themselves. In a sense, the quasinormal modes can be regarded as a characteristics sound of black holes. It is widely believed direct way to identify the existence of a black hole, when gravitational wave will be detected in the near future.
The thesis consists of five parts, and is organized as follows:
In Sec.1, a brief introduction of black hole's thermodynamic characters are given at first. Then, the definition, calculation method and motivations of study of the black hole entropy and quasinormal modes are introduced, respectively.
In Sec.2. firstly, the entropy of the charged dilaton-axion black hole is calculated for both asymptotically flat and non-flat cases, using the thin-film model. The thin-film model designates that the black hole entropy is contributed of quantum field by a thin film near the black hole horizon, and the results obtained confirm the Bekenstein-Hawking area-entropy formula. The thin-film model method avoids some drawbacks in the original brick-wall method, but the arbitrary cutoff to remove the divergence near the horizon cannot be avoided yet. For this, the entropy of black holes are corrected to leading order in the Planck length, with the newly modified equation of states density motivated by the generalized uncertainty principle, in the regime of the thin-film model method, which drastically solves the ultraviolet divergences of the just vicinity near the horizon replacing the conventional brick-wall method cutoff with the minimal length. Then, the integral equation of entropy can be solved with residue theorem, which is proportional to the black hole horizon area.
In Sec.3, adopting three-order WKB approximation method, the quasinormal modes of a black hole with a global monopole surrounded by static spherically-symmetric quintessence matter are calculated, for massive scalar fields and massless Dirac fields perturbation, re-spectively, and the influence of different parameters on quasinormal modes frequency are discussed.
In Sec.4, in the deformed Horava-Lifshitz gravity, the black hole quasinormal modes of the massless Dirac field perturbation are calculated, and then the influence of Horava-Lifshitz parameter on quasinormal modes frequency are discussed.
A conclusion is presented in the last section.
引文
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