黑洞霍金辐射、对偶性及相关问题的研究

发布时间：2019-04-03 18:02

【摘要】：本文综述了黑洞的基本知识和到目前为止所取得的研究成果,并详细介绍作者博士期间在黑洞霍金隧穿辐射、面积量子化以及对偶性这三个方面的研究工作。本文分为七章,具体内容如下: 第一章是综述部分。我们在该章对黑洞的形成、蒸发、热力学性质和探索等方面进行了阐述。第二章目的是将Parikh、Wilczek的工作推广到荷电粒子的霍金辐射。我们采用半经典量子隧穿方法对Einstein-Maxwell-Dilaton-Axion(EMDA)时空中标量荷电粒子的霍金辐射进行研究,其结果表明霍金辐射谱不是纯热谱,粒子隧穿率与Bekenstein-Hawking熵变有关。这与Parikh、Wilczek以及张靖仪等人的结果一致。同时,采用路径积分方法对Taub-Nut时空中带质量粒子的隧穿行为进行了研究,得到黑洞的霍金温度与以前的结果一致。第三章讨论费米子隧穿辐射。这部分内容关键是构造伽马矩阵。对于轴对称黑洞,考虑到视界附近能层中的物质场被拖曳着进行运动和伽马矩阵构造的方便性,我们在拖曳场中对费米子的隧穿辐射进行讨论。对de Sitter时空中费米子隧穿辐射的研究表明:具有正频的粒子在宇宙视界处的能量测得为负值。对Horava-Lifshitz引力理论中费米子隧穿辐射的研究表明:该引力理论的相关参数对黑洞霍金温度进行了约束。第四章,考虑到Nation等人关于一维量子通道描述光子的霍金辐射和Bekenstein、Mayo对黑洞维数约束的工作,我们将黑洞约束为一维,采用一维通道同时对Kerr和Kerr-Newman时空中费米子和玻色子的霍金辐射进行讨论。同时,对黑洞的热导率和电导率进行了研究,其结果表明:热导率只与黑洞表面引力有关,且不均匀;电导率只与粒子的电荷有关。在讨论中,隧穿粒子的磁量子数被视为广义的荷,相应的化学势等于磁量子数乘以角速度。第五章,结合Maggiore关于QNMs的新解释和黑洞热力学第一定律,我们对de Sitter时空中Schwarzschild黑洞和高维Reissner-Nordstrom黑洞在接近极端情况下的面积谱进行了讨论。其结果表明,面积谱和熵谱是等间隔的,与黑洞的参数无关。该结果具有普遍性,对于其它非极端黑洞同样适用。第六章是Kerr/CFT对应的进一步延伸。我们对EMDA黑洞在极端和非极端情况下的对偶性进行了讨论,得到该黑洞“near”区域存在共形对称性,但由于矢量场的局域定义和方位角的周期性,这种对称被视为瞬时破缺。在非极端情况下,我们得到“near”区域的吸收截面,它精确地与二维共形场理论(CFT)中有限温度的吸收截面相等。通过Cardy公式得到黑洞微观熵与Bekenstein-Hawking面积-熵相等。在极端情况下,通过重新定义共形坐标,研究了CFT和无质量标量场空间解的对偶性。得到微观熵与面积-熵相等。第七章给出全文的总结和以后工作的一些设想。
[Abstract]:In this paper, the basic knowledge of black hole and the research achievements so far are reviewed, and the author's research work on Hawking tunneling radiation, area quantization and duality of black hole is introduced in detail. This paper is divided into seven chapters, the specific contents are as follows: the first chapter is a summary part. In this chapter, we discuss the formation, evaporation, thermodynamic properties and exploration of black holes. The purpose of the second chapter is to extend the work of Parikh,Wilczek to Hawking radiation of charged particles. We use semi-classical quantum tunneling method to study the Hawking radiation of scalar charged particles in Einstein-Maxwell-Dilaton-Axion (EMDA) space-time. The results show that the Hawking radiation spectrum is not pure thermal spectrum, and the tunneling rate of particles is related to the change of Bekenstein-Hawking entropy. This is consistent with the results of Parikh,Wilczek and Zhang Jingyi and others. At the same time, the tunneling behavior of particles with mass in Taub-Nut spacetime is studied by means of path integral method. The Hawking temperature of the black hole is in agreement with the previous results. In the third chapter, the fermion tunneling radiation is discussed. The key of this part is to construct gamma matrix. In the case of axisymmetric black holes, the tunneling radiation of fermions is discussed in the towed field, taking into account that the matter field in the energy layer near the horizon is towed for motion and the convenience of the gamma matrix construction. The study of fermion tunneling radiation in de Sitter space-time shows that the energy of particles with positive frequency in the cosmic horizon is negative. The study of the fermion tunneling radiation in Horava-Lifshitz 's gravitational theory shows that the Hawking temperature of the black hole is constrained by the relevant parameters of the theory of gravity. In chapter 4, considering the work of Nation et al on the Hawking radiation of one-dimensional quantum channel describing photons and the constraint of Bekenstein,Mayo on the dimension of black hole, we restrict the black hole to one-dimensional. The Hawking radiation of fermions and bosons in Kerr and Kerr-Newman spacetime is discussed by means of one-dimensional channels at the same time. At the same time, the thermal conductivity and conductivity of the black hole are studied. The results show that the thermal conductivity is only related to the surface gravity of the black hole, and the conductivity is only related to the charge of the particle. In the discussion, the magnetic quantum number of the tunneling particle is regarded as a generalized charge, and the corresponding chemical potential is equal to the magnetic quantum number multiplied by the angular velocity. In chapter 5, combined with Maggiore's new explanation of QNMs and the first law of black hole thermodynamics, we discuss the area spectrum of Schwarzschild black hole and high-dimensional Reissner-Nordstrom black hole in space when de Sitter is close to the extreme. The results show that the area spectrum and entropy spectrum are equispaced and independent of the parameters of the black hole. This result is universal and is also applicable to other non-extreme black holes. The sixth chapter is a further extension of Kerr/CFT correspondence. The duality of EMDA black hole in extreme and non-extreme cases is discussed, and the conformal symmetry exists in the "near" region of the black hole. However, due to the local definition of vector field and the periodicity of azimuth angle, this symmetry is regarded as instantaneous breaking. In the non-extreme case, we obtain the absorption cross section of the "near" region, which is exactly equal to the absorption cross section of the finite temperature in the two-dimensional conformal field theory (CFT). The microscopic entropy of black hole is equal to that of Bekenstein-Hawking area-entropy by Cardy formula. In extreme cases, by redefining conformal coordinates, the duality of solutions of CFT and massless scalar field space is studied. The microscopic entropy is equal to the area-entropy. Chapter VII gives a summary of the full text and some ideas for future work.
【学位授予单位】：电子科技大学
【学位级别】：博士
【学位授予年份】：2011
【分类号】：P145.8

【共引文献】