【作者】 吴双清；

【导师】 蔡勖；

【作者基本信息】 华中师范大学 ， 理论物理， 2002， 博士

【摘要】 自从Hawking在1974年发现黑洞并不是完全黑的而是可以从视界发射热辐射以来，在过去的四分之一多个世纪里，人们已经用许多不同的方法对各种黑洞的量子热性质进行了大量的研究。但是多数研究主要集中在对稳(静)态黑洞热效应的考察之上。由于天体物理学上的一个黑洞实际上会向外发射辐射或吸积其周围的物质，因而它是动态的，随时间而演化的。因此研究动态黑洞的热性质就比稳态情形更加富有意义。但是研究动态黑洞Hawking蒸发的工具非常有限，传统的计算重整化能动张量的方法只适用于球对称情形，而且只能作近似处理，因而用途非常局限，难以用于其它更一般的情况。 而赵峥教授建议的广义乌龟坐标变换法(GTCT)则与之不同，它可以用于对各种黑洞时空热性质的研究上，并且获得了很大的成功。但是就我们所知，在我们的工作出来以前，这个方法在研究动态Kerr(-Newman)黑洞和作加速运动的Kinnersley黑洞这两类时空中Dirac旋量粒子的Hawking辐射问题上尚有一定的困难。本文旨在解决这一困难，并进一步发展GTCT法，使其成为一个比较完整的理论体系，可以用于对一般黑洞时空中任意自旋粒子热效应的研究上。 本文主要探讨各种特定的黑洞时空中量子场的行为，其内容可以划分为两个部分：一是寻找已知的黑洞几何背景上各种量子场(例如Klein-Gordon标量场)方程的精确解。二是研究各种黑洞中量子场的热性质，主要是集中在对动态黑洞中Dirac粒子的Hawking辐射的研究上，需要说明的是本文只关心四维黑洞情形，不考虑其它维数的黑洞情形。全文共分九章。 第一章简要介绍与本文有关的黑洞基本理论，包括黑洞物理学发展的简要历史，四维黑洞解的的分类，黑洞视界附近的经典过程和量子效应，以及黑洞热力学定律。 在第二章中我们研究了稳态轴对称黑洞背景几何中Klein-Gordon场方程分离变量部分的精确解，表明了Kerr-Newman黑洞及Kerr-Sen黑洞中有质量复标量场方程的径向部分和角向部分均满足广义椭球波方程，而后者实际上就是合流的Heun方程。基于Laplace变换，给出了联系不同参数的两个解的一套积分方程。类似地，一般可以证明Plebanski-Demianski度规(Petrov D-型时空)微扰的无质量的任意自旋场方程满足广义Teukolsky方程，其分离变量部分可以变换为Heun方程的形式。 K撞＆AtAY士子伍比义 t沥画地JI）（儿r爪吐1爪仆＊川们T＼ 第三章首先回顾了Hawking效应发现的历史背景，解释了黑洞辐射发生的物－理机制，然后介绍椎导Hawking辐射的各种方法；以及与这个理论有关的胸研究和可能的实验检验方案． 在这四章中，重点介绍了DamourRuffilliS删an（DRS）方案，用这个方法研究了Sbllwarzsdsld静态黑洞中标量粒子和旋量粒子的Hawking蒸发．接着用它考察了怔DN。n黑洞外（内）视界上Klei。Gordon标量场和mr。旋量场的nawti。g辐射厂‘吸收”），并指出内视界可以看成一个反常的负温系统．利用第H章中导出的精确解，我们用指标法对标量场的Hawking蒸发重新作了研究，将B。deen－Carte。H。ing建立的 Ker。Ne、an黑洞外视界上的热力学四定律推广到Cau呐内视界上，并且讨论了转动带电的黑洞平衡辐射过程的四个量子守恒定律；引入了标量粒子的量子嫡和约化视界面积的这两个新概念．最后用指标法研究了 Kerrsen黑洞背景上标量粒子的Hawking＆应；指出 Kerrsen黑洞与KerrNewman黑洞虽然几何性质不同；但它们的热力学性质和量子热效应却极其相似． 余下的几章是这本论文的核，C主体部分，用广义乌龟坐标变换法研究了动态黑洞中高自旋粒子（Dirac粒子和先子）的Hawking辐射；发现动态Kerr（－Ne…an）黑洞存在自旋－转动耦合效应，作任意加速运动的Kinne‘ley黑洞有自放加速耦合效应出现．对于Vidya型球对称时空；我们发现在Eddington－Finkelstein（EF坐标系中Dira啦子和光子的Hawking辐射是不对称的．对于这类非静态的刺称黑洞；没有看到与自旋相关的量子热效应出现． 与稳态黑洞情形相比，考察动态黑洞的uawting蒸发更加困难．在利用orers法研究一般黑洞时空的量子热效应时，需要同时考虑对一阶方程和二阶方程作广义乌龟坐标变换处理，然后利用一阶方雕供的一阶导锨间的关系式去换掉二阶方程中的一阶导数交叉项，这样才能舱个分量满足的二阶方程在视界附近化为单一分量的标准波方程．这个步骤是讨论高自旋粒子的Hawking蒸发问题能够成功的关键之处，因为余下的工作完全可以按照D朋建议的方案去进行处理．第五章首先介绍赵岭等咋研究动态黑洞的Hawking辐射中对D肪方法的推广；然后阐明我们对这个方法继续发展的思想，并简帕这方面所做的工作以及得到的一些主要结果． 用这个发展了的DAs七hao－WuCai＊册ZWC）方法；在第六章中重新研究了Vldya型球对称黑洞中Dirac粒子和光子的量子热效应，表明在EF坐标系中 Hawking辐射对它们的不同赡是不对称的．另外，我们采用了不同的方法严格 n更多还原

【Abstract】 Ever since Hawking discovered in 1974 that a black hole is not completely black but can emit radiation from its event horizon, considerable efforts had been made to reveal the quantum thermal properties of various kinds of black holes by many different methods in the past quarter century. However, most of these researches were concentrated on studying the thermal effect of static or stationary black holes. Because a realistic black hole in astrophysics can radiate or absorb matter surrounding it, it is non-stationary and evolves in the time. Thus the studies of the thermal properties of non-stationary black holes are more meaningful than that of stationary ones. But there are very limited tools to deal with the Hawking evaporation of non-stationary black holes. The traditionary method by calculating the renormalized energy momentum tensor can be used only in the spherical symmetric case, and it deals with the problem in an approximate manner. Thus this method is of limited use and meets great difficulties in other most general cases.The method of generalized tortoise coordinate transformation (GTCT) suggested by Prof. Zhao Zheng is, however, very different from that one. It has been used successfully to investigate the thermal properties of all kinds of black hole space-times. Prior to our work, as to the best of our knowledge, this method still has some difficulties in dealing with the Hawking evaporation of Dirac particles in the non-stationary Kerr(-Newman) black holes and in the accelerating Kinnersley space-tunes. The aim of this thesis is to settle down this problem, to develop the GTCT method further, and to make it become a fairly integrated system so that it can be used to tackle with the thermal effect of particles with arbitrary spins in the most general space-times.The main topic of this thesis is to investigate the behaviors of quantum fields in all specific black hole space-times. It can be divided into two parts: one is to find exact solutions to miscellaneous wave equations of quantum fields such asKlein-Gordon scalar field on some known black hole background geometries. The other is to discuss the thermal effect of quantum fields in various kinds of black hole space-times, focusing on the Hawking radiation of Dirac particles in the non-stationary black holes. It should be noted that here we only concern about the four dimensional case, neglecting other dimensional black holes. This dissertation has nine chapters.Chapter 1 introduces concisely some essential black hole theories with relation to this dissertation, including a brief history of the developments of black hole physics, classification of four dimensional black hole space-times, classical processes and quantum effects near black hole event horizon and four laws of black hole thermodynamics.In Chapter 2, we study exact solutions of the separated parts of Klein-Gordon field equation on some stationary and axisymmetry black hole backgrounds. We demonstrate that the radial and angular parts of a massive scalar field equation in the Kerr-Newman and Kerr-Sen black hole space-tunes satisfies the generalized spheroidal wave equation which is, in fact, a confluent Heun equation. On the base of the Laplace transformation, we present a new set of integral equations that relate two solutions with different parameters. Analogically, it can be generally shown that perturbations of massless fields with arbitrary spins in the Plebanski-Demianski metric (space-time of Petrov D-type) satisfy the generalized Teukolsky equation and their separated parts can be transformed into the form of Heun equation.In the third chapter, we first review the history backgrounds about the discovery of Hawking effect, and explain the physical mechanism that leads to black hole radiation. Then we introduce various methods that can deduce Hawking radiation, some recent researches on this theory and possible experimental ansatz that may test Hawking radiation.Chapter 4 emphasizes the Damour-Ruffini-Sannan (DRS) method and apply it to discuss the Hawking e更多还原