黑洞辐射正则系综模型及相关问题研究

In this project, we investigate the canonical ensemble model: 1) We consider the emitted shell, which composed of a number of identical particles, as a thermodynamical system. As a large heat source, the black hole and the emitted shell constitute an isolated system. Using the canonical ensemble theory we obtain the distribution function, and then discuss the quantum tunneling radiation spectrum, and determine the statistical significance of the quantum tunneling radiation spectrum. 2) With this canonical ensemble model and taking into account the quantum correction to black hole entropy, we will correct the existing life-span formula of the black hole, and obtain a general formula for the black hole life-span. 3) With this canonical ensemble model of the black hole quantum tunneling, we will discussed the Bose-Einstein condensation near the event horizon and other issues. 4)With this model, we will also discuss the black hole entropy, the black hole information and other related issues..We will apply the entropic force model of the gravitational force, proposed by E. verlinde, to the black hole physics and cosmology, Especially we will use the basic assumptions and the basic methods of the entropic force theory to discuss related issues in black hole physics: 1)We would investigate the fluctuation of the entropic force and the application in black hole physics and cosmology. 2) Considering the horizon as a holographic screen, we will study the entropy flow, information flow near the horizon in the emission process of the particles. On this basis, the statistical entropy of black holes and the information puzzle in the process of black hole Hawking radiation will be studied too. 3) With the entropic force model of the gravitational force, we will study other related issues in black hole physics and cosmology.

探讨黑洞量子隧穿辐射的正则系综模型：1）将出射壳层看成多个粒子组成的热力学系统，黑洞看作大热源与出射壳层组成一个孤立系统，利用正则系综理论讨论其分布函数，进而讨论量子隧穿辐射谱，确定出量子隧穿辐射谱的统计意义；2）用此正则系综模型，在考虑黑洞熵的量子修正的情况下，对黑洞寿命的计算公式进行修正，得到一般情况下黑洞寿命计算公式；3）利用量子隧穿的正则系综模型讨论视界附近的玻色-爱因斯坦凝聚等问题；4）讨论黑洞熵、黑洞信息等其它相关问题。.将E.Verlinde提出的引力的熵力模型应用到黑洞物理学与宇宙学中，特别是利用其中的基本假设和基本方法讨论黑洞物理学中的有关问题：1）研究熵力的涨落及在黑洞物理学中的应用；2）将视界视作全息屏，研究粒子出射过程中的熵流、信息流，并在此基础上研究黑洞的统计熵，以及黑洞霍金辐射过程中的信息疑难；3）用熵力模型研究黑洞热力学及宇宙学中的其它问题。

本项目研究黑洞辐射正则系综模型及相关问题，解决了如下几个方面的问题：1）提出了与黑洞量子隧穿辐射相对应的正则系综模型，给出了量子隧穿辐射的一个统计解释；2）计算出了精确的黑洞量子隧穿辐射谱；3）计算出了与量子隧穿辐射谱对应的黑洞辐射寿命修正公式；4）用广义测不准原理修改并推广了斯特藩定理，将平直时空中黑体辐射的斯特藩定理推广到了弯曲时空，从而修改了以前关于黑洞寿命（按黑体辐射）的计算公式；5）推广了目前流行的爱因斯坦场方程热力学解法，并得出了更加一般的球对称解。本项目共计发表SCI学术论文15篇；培养青年教师1名，研究生6人；项目主持人位列Elsevier“2014年中国高被引学者榜单”。