黑洞时空中的似正规模和幂率拖尾
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摘要
黑洞物理学作为广义相对论与量子力学、粒子物理、弦理论、热力学和统计物理等诸多学科的交叉领域,在现代物理学中起着非常重要的作用。多年来,黑洞物理一直是人们极为关心的热门领域。然而黑洞物理学中还有许多问题人们尚未弄清楚,像黑洞熵的统计起源、黑洞信息疑难以及黑洞是否稳定等都是黑洞物理中非常重要而有待解决的问题。弄清这些问题,有助于现代物理学的发展,也有助于我们深入地认识自然。黑洞时空中的似正规模和幂率拖尾问题涉及到黑洞的认证和稳定性等问题。研究表明它还与AdS/CFT对应和Loop量子引力理论有着十分密切的联系。因此对黑洞时空中似正规模和幂率拖尾的研究具有很重要的意义。
本文采用数值方法(P(?)shl-Teller势近似法、WKB近似法和连续分数法)和单值法分别研究了某些特殊黑洞时空中的似正规模频谱,然后应用Green函数法研究了整体单极子黑洞时空中的耦合标量场的幂率拖尾行为。本文的主要结论有:
1、应用三阶WKB近似法,我们研究了被quintessence(一种暗能量的模型)包围的黑洞时空中标量场的似正规模频谱,发现它与这种暗能量的态参数(暗能量的压强和能量密度的比值)有关:当态参数的绝对值增大时,似正规模频谱的实部减小,而虚部的幅度增加。这表明暗能量的出现使标量场的衰减加快。因此暗能量对似正规模的振动起阻尼作用。
2、采用P(?)shl-Teller势近似法和连续分数法研究了Garfinkle-Horowitz-Strominger伸缩子黑洞时空中Dirac场的似正规模,我们发现当伸缩子
Black hole physics plays an important role in the modern physics as it is an intersectionsl field of general relative theory, quantum mechanics, particle physics, string theory, thermodynamics and statistics. However, there exist many open questions to be addressed in the black hole physics, such as the statistical origin of black hole entropy, the information puzzle and stability of black holes, and so on. The full comprehension of these problems will promote the development of the modern physics more rapidly and help us to understand the nature from the further levels. The quasinormal modes and the late-time tails of perturbational fields in the black hole spacetime are related to the identification and stability of the black holes. Moreover, it is also found that they are connected closely with the AdS/CFT correspondence and loop quantum gravity. Therefore, it is of great importance to investigate the quasinormal modes and the late-time tails in the black hole spacetimes.In this thesis, we first investigate the quasinormal modes of some special black holes by using some numerical methods (such as Poshl-Teller approximation, Wentzel-Kramers-Brillouin(WKB) approximation and continue fraction method) and monodromy technique. Then we adopt to Green function method and study the late-time tails of a coupled scalar field in the black hole spacetime with global monopole. Our main works are as follows:(1) Using the third-order WKB approximation, we evaluate the quasinormal modes of scalar field in the black hole spacetime surrounded by quintessence and
find that the quasinormal frequencies depend on the state parameter (i.e. the ratio between pressure and energy density of dark energy) of quintessence. As the absolute value of the state parameter increases, the real part of quasinormal frequencies decreases and the amplitude of the imaginary part increases. This means that the presence of dark energy makes scalar field damp more rapidly. It is also shown that dark energy restrains the oscillation of field in the black hole spacetime.(2) Adopting to the Poshl-Teller potential approximation and the continue fraction method, we investigate Dirac quasinormal modes in the Garfmkle-Horowitz-Strominger dilaton black hole spacetime. We find that as the paramter a of the dilaton field increases, the real parts of quasinormal frequencies increase, the imaginary part first increases and then decreases. When the overtone n is lower andI is larger, the space of the real part depends only on the parameter a and increases with the increase of a, but that of the imaginary part tends to zero. As the overtone n becomes larger, we find the imaginary part in direct proportion to the overtone n.(3) For the acoustic black hole, we study the quasinormal modes coupled scalar field by using the third-order WKB approximation, and find that, for the lower overtone, the real part increases and the imaginary part decreases as the coupled factor f increases. When f is larger, both the real and imaginary parts are almost the linear function of the coupled factor ￡.(4) In order to probe the universal validity of Hod conjecture, we adopt to the monodromy technique and investigate the asympotic quasinormal modes of the coupled scalar fields in the Garfinkle-Horowitz-Strominger, Gibbons-Maeda and acoustic black holes spacetimes and find their frequency formulas of high
damped quasinormal modes are related to the coupled factor ￡. It is shown that the high damped quasinormal frequencies depend not only on the parameters of black hole spacetimes, but also on the coupled strength between the scalar field and the background metric. This means that Hod conjecture is not valid universally.(5) At last, we study the late-time tails of a coupled scalar field in the space-time of black hole with a global monopole. For the Schwarzschild, Reissner-Nordstrom black holes, the decay factor of the late-time tails depends only on the multiple moment / and the mass \x of perturbationaJ field. However, in the spacetime of black hole with a global monopole, we find that the decay factor depends not only on the the multiple moment I and the mass /n, but also on the coupling between the scalar field and the background spacetime. Furthermore, the scalar field decays more rapidly as the coupled factor ￡ increases.
本文采用数值方法(P(?)shl-Teller势近似法、WKB近似法和连续分数法)和单值法分别研究了某些特殊黑洞时空中的似正规模频谱,然后应用Green函数法研究了整体单极子黑洞时空中的耦合标量场的幂率拖尾行为。本文的主要结论有:
1、应用三阶WKB近似法,我们研究了被quintessence(一种暗能量的模型)包围的黑洞时空中标量场的似正规模频谱,发现它与这种暗能量的态参数(暗能量的压强和能量密度的比值)有关:当态参数的绝对值增大时,似正规模频谱的实部减小,而虚部的幅度增加。这表明暗能量的出现使标量场的衰减加快。因此暗能量对似正规模的振动起阻尼作用。
2、采用P(?)shl-Teller势近似法和连续分数法研究了Garfinkle-Horowitz-Strominger伸缩子黑洞时空中Dirac场的似正规模,我们发现当伸缩子
Black hole physics plays an important role in the modern physics as it is an intersectionsl field of general relative theory, quantum mechanics, particle physics, string theory, thermodynamics and statistics. However, there exist many open questions to be addressed in the black hole physics, such as the statistical origin of black hole entropy, the information puzzle and stability of black holes, and so on. The full comprehension of these problems will promote the development of the modern physics more rapidly and help us to understand the nature from the further levels. The quasinormal modes and the late-time tails of perturbational fields in the black hole spacetime are related to the identification and stability of the black holes. Moreover, it is also found that they are connected closely with the AdS/CFT correspondence and loop quantum gravity. Therefore, it is of great importance to investigate the quasinormal modes and the late-time tails in the black hole spacetimes.In this thesis, we first investigate the quasinormal modes of some special black holes by using some numerical methods (such as Poshl-Teller approximation, Wentzel-Kramers-Brillouin(WKB) approximation and continue fraction method) and monodromy technique. Then we adopt to Green function method and study the late-time tails of a coupled scalar field in the black hole spacetime with global monopole. Our main works are as follows:(1) Using the third-order WKB approximation, we evaluate the quasinormal modes of scalar field in the black hole spacetime surrounded by quintessence and
find that the quasinormal frequencies depend on the state parameter (i.e. the ratio between pressure and energy density of dark energy) of quintessence. As the absolute value of the state parameter increases, the real part of quasinormal frequencies decreases and the amplitude of the imaginary part increases. This means that the presence of dark energy makes scalar field damp more rapidly. It is also shown that dark energy restrains the oscillation of field in the black hole spacetime.(2) Adopting to the Poshl-Teller potential approximation and the continue fraction method, we investigate Dirac quasinormal modes in the Garfmkle-Horowitz-Strominger dilaton black hole spacetime. We find that as the paramter a of the dilaton field increases, the real parts of quasinormal frequencies increase, the imaginary part first increases and then decreases. When the overtone n is lower andI is larger, the space of the real part depends only on the parameter a and increases with the increase of a, but that of the imaginary part tends to zero. As the overtone n becomes larger, we find the imaginary part in direct proportion to the overtone n.(3) For the acoustic black hole, we study the quasinormal modes coupled scalar field by using the third-order WKB approximation, and find that, for the lower overtone, the real part increases and the imaginary part decreases as the coupled factor f increases. When f is larger, both the real and imaginary parts are almost the linear function of the coupled factor ￡.(4) In order to probe the universal validity of Hod conjecture, we adopt to the monodromy technique and investigate the asympotic quasinormal modes of the coupled scalar fields in the Garfinkle-Horowitz-Strominger, Gibbons-Maeda and acoustic black holes spacetimes and find their frequency formulas of high
damped quasinormal modes are related to the coupled factor ￡. It is shown that the high damped quasinormal frequencies depend not only on the parameters of black hole spacetimes, but also on the coupled strength between the scalar field and the background metric. This means that Hod conjecture is not valid universally.(5) At last, we study the late-time tails of a coupled scalar field in the space-time of black hole with a global monopole. For the Schwarzschild, Reissner-Nordstrom black holes, the decay factor of the late-time tails depends only on the multiple moment / and the mass \x of perturbationaJ field. However, in the spacetime of black hole with a global monopole, we find that the decay factor depends not only on the the multiple moment I and the mass /n, but also on the coupling between the scalar field and the background spacetime. Furthermore, the scalar field decays more rapidly as the coupled factor ￡ increases.
引文
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