霍金辐射和黑洞熵

发布时间：2018-04-03 17:20

本文选题：黑洞　切入点：霍金辐射　出处：《大连理工大学》2010年博士论文

【摘要】： 从上世纪70年代发现霍金辐射至今,对黑洞的研究已经取得了长足的进展。虽然尚未确证黑洞的存在,但对黑洞的理论研究已经揭示出一些涉及物理学和哲学基本观念的问题,具有划时代的意义。论文首先介绍了霍金辐射出现的的历史背景及其所带来的信息疑难问题,即量子纯态演化为热混合态,违背了量子力学中的幺正性原理。接着介绍了解决信息疑难问题的一种比较好的方法-派瑞克方法。其出发点是将黑洞的霍金辐射理解成一种量子隧穿,势垒强弱取决于出射粒子自身能量的大小。用这种方法,派瑞克等人计算了零质量粒子穿过Schwarschild黑洞和Reissner-Nordstrom黑洞的出射修正谱。结果显示粒子的隧穿几率和贝根斯坦-霍金熵的变化量有关,出射谱线偏离纯热谱,满足幺正性原理,支持信息守恒。接下来把派瑞克方法的推广到了更一般的稳态黑洞。此外哈密顿-雅克比方法揭示了派瑞克方法的一些不足之处,即用雅克比方法得到的黑洞温度与霍金得到的并不一致,是后者的两倍。为了解决这一难题,论文引入了各项同性坐标系。考虑了入射粒子的贡献,得到了正确的霍金温度,并证明了在派瑞克方法使用的坐标系(Painleve-Gullstrand坐标系)中入射粒子的贡献为零。接下来介绍了黑洞熵的一些性质。根据黑洞热力学第二定律,黑洞熵在数值上等于黑洞表面积的四分之一,且在顺时方向上永不减少。黑洞外部并不是平静的,充满了扰动场。一般来说,扰动场对黑洞熵的影响表现为黑洞熵公式中增加的一个对数修正项。修正项中的系数和扰动场的模型有关,是待定的。第三章在正则系统中引入拉普拉斯方法计算了热场扰动对黑洞熵的修正,因为正则系统允许黑洞和外界热场有能量的交换。论文还介绍了另外一套方法,这种方法的主要特点是将黑洞看成一个处在热场中的盒子,那么黑洞就会和它周围的物质达到热平衡状态。论文将这种方法应用到了不同维度的各种黑洞时空当中,得到了一些有用的结果。最后引入了随动坐标系的观测者,得出了Schwarzschild黑洞在热场扰动下,随动观测者观测到的黑洞熵和他所处的位置有关。最后,介绍了广义不确定原理。经研究证实,当引力效果很弱的时候,广义不确定原理可以退化成海森堡不确定关系；当引力场强度不能忽略的时候,海森堡不确定关系不能替代广义不确定原理。根据广义不确定原理,位置的不确定度存在一个最小值。论文用广义不确定原理研究了量子场扰动对Schwarzschild黑洞熵和温度的影响。接下来论文引入了推广的不确定原理(EUP、GEUP)和修正的不确定原理(MDR),并在各种黑洞时空中进行了推广,得到了一些比较有用的结果并进行了分析。
[Abstract]:Since the discovery of Hawking radiation in the 1970s, considerable progress has been made in the study of black holes.Although the existence of black hole has not been confirmed, the theoretical study of black hole has revealed some problems related to the basic concepts of physics and philosophy, which is of epoch-making significance.This paper first introduces the historical background of Hawking radiation and the information problems it brings, that is, the evolution of pure quantum states into thermal mixed states, which is contrary to the unitary principle of quantum mechanics.Then it introduces a better method to solve the problem of information-Parrack method.The starting point is to interpret the Hawking radiation of a black hole as a kind of quantum tunneling.Using this method, Parrack et al calculated the emission correction spectra of zero mass particles passing through Schwarschild black holes and Reissner-Nordstrom black holes.The results show that the tunneling probability of particles is related to the change of Baygenstein-Hawking entropy. The emission line deviates from the pure heat spectrum, satisfies the unitary principle, and supports the conservation of information.Then the Parrack method is extended to a more general stationary black hole.In addition, the Hamilton-Jacobian method reveals some shortcomings of the Parrack method, that is, the temperature of the black hole obtained by the Jacobian method is not consistent with that obtained by Hawking, and is twice that of the latter.In order to solve this problem, the same-sex coordinate system is introduced in this paper.Considering the contribution of incident particles, the correct Hawking temperature is obtained, and it is proved that the contribution of incident particles in the Painleve-Gullstrand coordinate system used in the Parrack method is zero.Then some properties of black hole entropy are introduced.According to the second law of black hole thermodynamics, the entropy of the black hole is equal to 1/4 of the surface area of the black hole numerically, and will never decrease in the chronological direction.The outside of the black hole is not calm and full of disturbance fields.Generally speaking, the effect of perturbation field on black hole entropy is expressed as a logarithmic correction term added to the black hole entropy formula.The coefficients in the modified term are dependent on the model of the perturbation field and are to be determined.In the third chapter the Laplace method is introduced into the positive system to calculate the modification of the entropy of the black hole due to the disturbance of the thermal field because the regular system allows the exchange of energy between the black hole and the external thermal field.The paper also introduces another set of methods. The main feature of this method is that the black hole is regarded as a box in the thermal field, then the black hole and the surrounding matter will reach the state of thermal equilibrium.This method is applied to black hole space-time in different dimensions, and some useful results are obtained.Finally, the observators of the following coordinate system are introduced, and the entropy of the Schwarzschild black hole observed by the follower under the disturbance of the thermal field is related to the position of the black hole.Finally, the generalized uncertainty principle is introduced.It is proved that when the gravitational effect is very weak, the generalized uncertainty principle can be degenerated into Heisenberg uncertainty relation, and when the gravitational field intensity cannot be ignored, the Heisenberg uncertainty relation cannot replace the generalized uncertainty principle.According to the generalized uncertainty principle, there exists a minimum value for the uncertainty of position.In this paper, the effect of quantum field perturbation on the entropy and temperature of Schwarzschild black hole is studied by using the generalized uncertainty principle.Then the generalized principle of uncertainty (EUPGE-UPU) and the modified principle of uncertainty (MDR ~ +) are introduced and generalized in various black hole space-time. Some useful results are obtained and analyzed.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2010
【分类号】：P145.8

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