宇宙学和致密天体相关问题的理论研究
摘要
在本文中,我们基于实验观测数据研究了暗能量模型和致密天体的一些物理性质,包括黑洞的可观测信号,热力学和相变,以及慢转奇异星。
为了解释宇宙微波背景辐射(CMB)功率谱在小l下的压低行为,我们将全息原理引入宇宙学的研究中。在此原理下得出的CMB功率谱在小l下的行为同WMAP实验观测数据相一致,这显示了全息原理即使在宇宙学尺度上依然有效。我们还利用这个原理对一些暗能量模型的参数和其演化给出约束。
在关于现代加速膨胀宇宙的讨论中,我们还建立一个以Dirac大数假说为基础的,能够统一广义相对论和Dirac宇宙学的模型。我们用超新星数据来拟合模型参数后,计算了一些宇宙学物理量。我们的结果同现代实验观测符合的相当好,并且强烈暗示着两点:1)“引力常数”在宇宙学尺度上并非常数,现在正在随时间流逝而减小;2)所谓的“暗能量”、“暗物质”其实就是Dirac宇宙学中的附加创生物质和多重创生物质。我们的模型与同太阳系中的实验相容。
为了在实验中考察是否存在额外维度,我们研究了在带有潮汐荷的膜世界黑洞背景下,标量扰动和膜上的引力扰动的准正则模式和Hawking辐射。与普通四维黑洞背景比较后,我们发现无论是准正则模式还是Hawking辐射,都可以体现出额外维度所产生的效应。这为以后的实验验证是否存在额外维度提供了理论依据。
我们重新检验了准正则模可以体现黑洞相变的观点,考察了拓扑黑洞和带标量场黑洞背景下的标量场准正则模式在相变点附近的行为,结果发现准正则模式可以体现这个相变过程。为更进一步了解一般的黑洞相变与准正则模式的关系。我们计算了平坦AdS黑洞和AdS孤子解时空下相变附近的准正则模,但发现准正则模无明显变化。因此,准正则模式能否体现一般黑洞的相变过程还值得更加细致的推敲。
为进一步理解黑洞相变的热力学,我们将Ruppeiner的热力学几何理论运用到黑洞热力学中。基于RN-AdS黑洞和van der Waals气液系统的相似性,我们把Ruppeiner度规作为黑洞内能和电场(或角速度)的函数,计算了RN,Kerr和RN-AdS黑洞的Ruppeiner几何。我们的结果与Davies相变的观点很好地符合,我们还用Ruppeiner几何考察了黑洞相变临界行为。
在对奇异星的研究中,我们利用夸克质量密度温度相关模型给出的夸克物质的状态方程和Hartle处理慢速转动天体的方法来构建一个热的缓慢转动的奇异星,考察了它的质量半径关系,转动惯量和参照系拖动效应等,并且发现对于奇异星,温度和转动频率都对天体结构有着重要影响。我们还将Hartle方法拓展到了差动转动情况。
In this dissertation, we study the models of dark energy based on the observational data and the properties of the highly dense astronomic objects, including the observational signals, the thermodynamics and phase transitions of black holes, slowly rotating strange star.
To explain the recent observational data of the suppression of the CMB power spectrum at small l, we employ the holographic cosmic duality to study the cosmology. We obtain a reasonable agreement between the holographic predictions of CMB at small l and the WMAP observation, showing the power of the holographic idea. We also use this idea to constrain some models of dark energy and their evolutions.
We have established a model on the modern accelerating universe, inspired by the Dirac's Large Number Hypothesis. This model can unify the Einstein general relativity and Dirac cosmology. After adjusting the model parameters by using the supernova data, we calculate a series of cosmological quantities. Our results agree the recent observation data well and suggest that 1) " the gravitational constant" is not a constant on the cosmological scale and actually is decreasing by time; 2) the addition creation and multiplication creation in Dirac cosmology are the dark energy and dark matter respectively. We have shown that our theory is consistent with the solar system tests.
In order to verify the existence of the extra dimensions in the experiments, we study the Quasi-Normal Modes (QNM) and the Hawking radiation for both scalar and brane-localized gravitational perturbations in the background of a brane-world black hole with a tidal charge. Comparing with four-dimensional black holes, we have observed that the signature of the tidal charge can present the effects of the extra dimensions both in the QNM and the Hawking radiation. Our results provide theoretical investigations on the existence of the extra dimensions for the future experimental observations.
We also reexamined the argument that the QNM could be a probe of the phase transition of black hole. We investigate the behavior of QNM near the critical point of the black hole phase transition between a topological black hole and a hairy black hole. We find the evidence that QNM can reflect this phase transition. Further, we calculate the QNM near the critical point of phase transition between a flat AdS black hole and an AdS soliton spacetime, in order to understand the relation between black hole phase transition and QNM. But we do not find any dramatic changes at the critical point. Therefore, the original argument should be investigated in subtler studies.
To understand black hole's phase transition and its thermodynamics, we introduce Ruppeiner's thermodynamic geometry into the thermodynamics of black hole. Based on the analogy between the RN-AdS black holes and the van der Waals-Maxwell liquid-gas system, we study the Ruppeiner geometry whose metrics are the functions with respect to the internal energy of black hole and electric potential(angular velocity), for RN, Kerr and RN-AdS black holes. Our results are in good agreement of the Davies' phase transition. We also study the critical behavior with the Ruppeiner geometry.
In the study of strange star, we employ the equation of state of strange matter induced by the Quark Mass Density- and Temperature- Dependent model and Hartle's method to configure hot and slowly rotating strange star. We investigate the star's mass-radius relation, the moment of inertia and the frame dragging and find some important influences of temperature and rotating frequency on the configuration of star. We also extend the Hartle's method to the differential rotating star.
为了解释宇宙微波背景辐射(CMB)功率谱在小l下的压低行为,我们将全息原理引入宇宙学的研究中。在此原理下得出的CMB功率谱在小l下的行为同WMAP实验观测数据相一致,这显示了全息原理即使在宇宙学尺度上依然有效。我们还利用这个原理对一些暗能量模型的参数和其演化给出约束。
在关于现代加速膨胀宇宙的讨论中,我们还建立一个以Dirac大数假说为基础的,能够统一广义相对论和Dirac宇宙学的模型。我们用超新星数据来拟合模型参数后,计算了一些宇宙学物理量。我们的结果同现代实验观测符合的相当好,并且强烈暗示着两点:1)“引力常数”在宇宙学尺度上并非常数,现在正在随时间流逝而减小;2)所谓的“暗能量”、“暗物质”其实就是Dirac宇宙学中的附加创生物质和多重创生物质。我们的模型与同太阳系中的实验相容。
为了在实验中考察是否存在额外维度,我们研究了在带有潮汐荷的膜世界黑洞背景下,标量扰动和膜上的引力扰动的准正则模式和Hawking辐射。与普通四维黑洞背景比较后,我们发现无论是准正则模式还是Hawking辐射,都可以体现出额外维度所产生的效应。这为以后的实验验证是否存在额外维度提供了理论依据。
我们重新检验了准正则模可以体现黑洞相变的观点,考察了拓扑黑洞和带标量场黑洞背景下的标量场准正则模式在相变点附近的行为,结果发现准正则模式可以体现这个相变过程。为更进一步了解一般的黑洞相变与准正则模式的关系。我们计算了平坦AdS黑洞和AdS孤子解时空下相变附近的准正则模,但发现准正则模无明显变化。因此,准正则模式能否体现一般黑洞的相变过程还值得更加细致的推敲。
为进一步理解黑洞相变的热力学,我们将Ruppeiner的热力学几何理论运用到黑洞热力学中。基于RN-AdS黑洞和van der Waals气液系统的相似性,我们把Ruppeiner度规作为黑洞内能和电场(或角速度)的函数,计算了RN,Kerr和RN-AdS黑洞的Ruppeiner几何。我们的结果与Davies相变的观点很好地符合,我们还用Ruppeiner几何考察了黑洞相变临界行为。
在对奇异星的研究中,我们利用夸克质量密度温度相关模型给出的夸克物质的状态方程和Hartle处理慢速转动天体的方法来构建一个热的缓慢转动的奇异星,考察了它的质量半径关系,转动惯量和参照系拖动效应等,并且发现对于奇异星,温度和转动频率都对天体结构有着重要影响。我们还将Hartle方法拓展到了差动转动情况。
In this dissertation, we study the models of dark energy based on the observational data and the properties of the highly dense astronomic objects, including the observational signals, the thermodynamics and phase transitions of black holes, slowly rotating strange star.
To explain the recent observational data of the suppression of the CMB power spectrum at small l, we employ the holographic cosmic duality to study the cosmology. We obtain a reasonable agreement between the holographic predictions of CMB at small l and the WMAP observation, showing the power of the holographic idea. We also use this idea to constrain some models of dark energy and their evolutions.
We have established a model on the modern accelerating universe, inspired by the Dirac's Large Number Hypothesis. This model can unify the Einstein general relativity and Dirac cosmology. After adjusting the model parameters by using the supernova data, we calculate a series of cosmological quantities. Our results agree the recent observation data well and suggest that 1) " the gravitational constant" is not a constant on the cosmological scale and actually is decreasing by time; 2) the addition creation and multiplication creation in Dirac cosmology are the dark energy and dark matter respectively. We have shown that our theory is consistent with the solar system tests.
In order to verify the existence of the extra dimensions in the experiments, we study the Quasi-Normal Modes (QNM) and the Hawking radiation for both scalar and brane-localized gravitational perturbations in the background of a brane-world black hole with a tidal charge. Comparing with four-dimensional black holes, we have observed that the signature of the tidal charge can present the effects of the extra dimensions both in the QNM and the Hawking radiation. Our results provide theoretical investigations on the existence of the extra dimensions for the future experimental observations.
We also reexamined the argument that the QNM could be a probe of the phase transition of black hole. We investigate the behavior of QNM near the critical point of the black hole phase transition between a topological black hole and a hairy black hole. We find the evidence that QNM can reflect this phase transition. Further, we calculate the QNM near the critical point of phase transition between a flat AdS black hole and an AdS soliton spacetime, in order to understand the relation between black hole phase transition and QNM. But we do not find any dramatic changes at the critical point. Therefore, the original argument should be investigated in subtler studies.
To understand black hole's phase transition and its thermodynamics, we introduce Ruppeiner's thermodynamic geometry into the thermodynamics of black hole. Based on the analogy between the RN-AdS black holes and the van der Waals-Maxwell liquid-gas system, we study the Ruppeiner geometry whose metrics are the functions with respect to the internal energy of black hole and electric potential(angular velocity), for RN, Kerr and RN-AdS black holes. Our results are in good agreement of the Davies' phase transition. We also study the critical behavior with the Ruppeiner geometry.
In the study of strange star, we employ the equation of state of strange matter induced by the Quark Mass Density- and Temperature- Dependent model and Hartle's method to configure hot and slowly rotating strange star. We investigate the star's mass-radius relation, the moment of inertia and the frame dragging and find some important influences of temperature and rotating frequency on the configuration of star. We also extend the Hartle's method to the differential rotating star.
引文
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