Kerr黑洞隧穿辐射的新处理

New treatment on tunneling radiation from Kerr black holes

自2000年Parikh和Wilczek采用半经典隧穿图像研究了静态球对称黑洞的Hawking辐射之后,其工作受到了极大的关注并被推广到各种情形.但是在几乎所有后来的工作中,存在两个重要的缺陷:(1)与无质量粒子的情形不同的是,对有质量粒子的测地线方程采用了不同的、而且非常牵强的推导方法;(2)对转动黑洞的隧穿辐射处理需要在拖曳坐标系中进行分析.本文采用新的思路对Kerr黑洞隧穿辐射重新作了研究,即利用Lagrange分析方法对Kerr黑洞中的有质量粒子和无质量粒子的测地线运动作了自洽的、统一的、新的处理,同时克服了上述两个重大缺陷,使得Parikh-Wilczek方法更加完善.

Since Parikh and Wilczek adopted a semi-classical tunnelling picture to investigate Hawking radiation of static and spheri- cally symmetric black holes in the year of 2000, their work had been paid much attention to and extended to various other cases. However, in almost all of the subsequent papers, there exist two important shortcomings： （1） different from the massless case, one has to use a different and very lame approach to derive the geodesic equation obeyed by the massive particles; （2） to deal with the tunnelling radiation of a rotating black hole, one is limited to use the dragging coordinates to do the job. In this paper, we shall adopt a new idea to re-investigate the tunnelling radiation of the Kerr black holes, that is, by applying the method of Lagrangian analysis in Classical Mechanics, we will make a new, consistent and unified treatment on the geodesics of massive and massless particles from Kerr black holes. Moreover, we can simultaneously overcome the two main defects mentioned above, thus making Parikh-Wilczek＇s semi-classical approach more perfect and consistent.