【作者】 张宇；

【导师】 桂元星；

【作者基本信息】 大连理工大学 ， 理论物理， 2006， 硕士

【摘要】 爱因斯坦的广义相对论预言了黑洞的存在,但由于黑洞的一些特性使得对它的探测极为困难。人们在某些双星系中发现了致密天体,分析表明这些天体的质量远远超出了广义相对论中任何一颗死亡恒星的质量极限,因而把它们确定为黑洞。如果黑洞本身有辐射,而且我们能够通过某种手段观测得到,不仅能够说明黑洞的存在,还能对它的结构有所了解。这样,我们可以假定黑洞时空中存在辐射场,对它的性质进行研究,从而加深对黑洞的理解。 本文的主要内容是关于黑洞视界外部时空中的标量场,我们选择的黑洞时空在无穷远处是渐近de Sider时空。在论文的第一章,简单地介绍了黑洞的形成、视界的概念、黑洞的热性质以及黑洞辐射和标量场辐射等基础知识。 在第二章中我们计算了在Schwarzschild-de Sider时空中对应不同的角频率ω下的实标量场方程。计算中使用了多项式拟合的方法来推导乌龟坐标x和半径r的关系。结果显示场方程的曲线近似简偕波,并且曲线的波长和频率随着角频率ω改变而改变。在这一章中,我们还对反射、透射系数的计算方法进行了讨论。 第三章则介绍Hisao Suzuk,Eiichi Takasugi和Hiroshi Umetsu在Kerr-Newman-de Sitter时空中无质量场方程的解析解法。Hisao Suzuk等通过一系列参量变换转化Teukolsky方程为Heun方程,而Heun方程是已知的数理方程,其解的形式是超几何函数级数。他们的解析解法对我们寻求标量场方程的解析解有着重要的启发意义。更多还原

【Abstract】 Black hole is one of the predictions of Einstein’s general relativity, but it is very hard to detect because the characters of black holes. People found compact objects in some binary systems, and identified them as black holes, because careful analysis showed that their masses are far beyond any limit accepted for dead stars in general relativity. If black holes have some characteristic radiation outside the event horizon, then a high precision can be expected to identify them and also to understand their inner structure.This dissertation is mainly about the scalar field in curved black hole spacetime backgrounds assumed to be asymptotic de Sitter space at infinity. In the first chapters, the concepts of black hole and the event horizon, black hole radiation ,the thermal properties of black hole, and scalar field radiation are introduced briefly.In chapter 2, the real scalar field equation is solved numerically in Schwarzchild-de Sitter space-time with different angular frequency co. A method called 憄olynomial? approximation is used to derive the relation between the tortoise coordinate x and the radius r. It抯found that the wave function is close to that of a harmonic wave. And when co alters, the curve抯amplitude and wavelength are different. The method of calculating the reflection and transmission coefficients is also discussed in this chapter.In chapter 2, the analytic solution of massless field equation in Kerr-Newman-de Sitter Spacetime which is given by Hisao Suzuk, Eiichi Takasugi and Hiroshi Umetsu is introduced. The Teukolsky equation is transformed to Heun eqution by variable substitution, and the Heun eqution is a known mathematical function, its solutions is in the form of series of hypergeometric functions. This method is helpful for us to find the way of the analytic solution of scalar field equation.更多还原