动态球对称时空和动态平面对称时空中时间尺度变换的补偿效应 *

动态球对称时空和动态平面对称时空中的Hawking效应都可看作时间尺度变换下的补偿效应.纯规范势的一个分量与稳态时空相同,表征黑洞温度.另一个在稳态情况为零的分量,现以非零的简洁形式出现,表征黑洞温度的变化率.     

球对称带电时空中Dirac粒子的Hawking效应

该文避开求解能－动张量的困难，在视界附近直接求解Ｄｉｒａｃ方程，得到球对称带电黑洞的事件视界位置和Ｈａｗｋｉｎｇ辐射温度．进一步分析表明Ｈａｗｋｉｎｇ辐射温度是时间坐标尺度变换下的补偿效应．     

准静态蒸发带电黑洞的量子热效应

把对动态黑洞量子热效应的研究推广到用(t，r)坐标描述的时空.采用了既不同于稳态又不同于以超前Eddington坐标v描述的动态时空的乌龟坐标方程.在考虑Hawking蒸发影响的情况下,得到了黑洞的温度、视界位置.进一步分析表明Hawking辐射温度是坐标尺度变换下的补偿效应.     

3—Sasakian流形的3—C—全实子流形

引入并研究了３－Ｓａｓａｋｉａｎ流形的３－Ｃ－全实子流形，借助了第二基本形式的长度，给出了单位球面Ｓ＾４ｍ＋３－Ｃ－全实子流形的一个Ｐｉｎｃｈｉｎｇ定理。     

黑洞附近修正的Stefan—Boltzmann定律

该文在一般球对称静态黑洞背景下,用WKB近似法得到黑洞附近修正的Stefan-Boltzmann定律.发现在黑洞事件视界附近,由于场自旋的存在,结果中除了类似于平直时空的主导项外,多了一个和局域温度二次方成正比的附加项.该项的出现暗示黑洞的辐射可能不是精确热的.     

准静态蒸发Kerr黑洞的量子热效应

该文采用新的广义乌龟坐标变换后,在事件视界附近直接求解Klein-Gordon方程,得到以(t,r)坐标描述的轴对称Kerr黑洞的视界位置、辐射温度.计算结果表明,考虑蒸发后Kerr黑洞的视界面是一个随时间变化的椭球面,Hawking辐射温度不仅随时间变化,而且与方位角有关.进一步分析表明Hawking辐射温度是时间坐标尺度下的补偿效应.     

一个静态Gutsunaev—Manko黑洞视界温度的计算方法

计算出了一个新的静态Gutsunaev-Manko黑洞的视界温度，其结果表明，此黑洞存在热辐射，除了内禀奇点所在处之外，视界温度是常数，黑洞质量多极矩的存在将对内禀奇点处的视界温度产生很大影响．     

Artin半单环的特征

本文证明了如下结果：环Ｒ是Ａｒｔｉｎ半单的当且仅当存在一个基数ｃ，使得任意左Ｒ－模是一个连续模和一个ｃ－限制的ＥＳ－模的直和，也当且仅当存在一个基数ｃ，使得任意左界Ｒ－模是一个拟投射模和一个ｃ－限制的ＥＳ－模的直和。     

Quasi—conformally Flat Manifolds with Constant Scalar Curvature

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＭｂｅａｎｎ－ｄｉｍｅｎｓｉｏｎａｌｃｏｎｆｏｒｍａｌｌｙｆｌａｔｍａｎｉｆｏｌｄｗｉｔｈｃｏｎｓｔａｎｔｓｃａｌａｒｃｕｒｖａｔｕｒｅρ（ｎ≥３）．ＷｈｅｎｔｈｅＲｉｃｃｉｃｕｒｖａｔｕｒｅＳｏｆＭｉｓｏｆｂｏｕｎｄｅｄｂｅｌｏｗａｎｄｙＳｙ２＜ρ２／（ｎ－１），Ｇｏｌｄ－ｂｅｒｇｐｒｏｖｅｄｔｈａｔＭｉｓｏｆｃｏｎｓｔａｎｔｃｕｒｖａｔｕｒｅ［１］．ＷｈｅｎＭｉｓａｃｏｍｐａｃｔｍａｎｉｆｏｌｄｗｉｔｈｐｏｓｉｔｉｖｅＲｉｃｃｉｃｕｒｖａｔｕｒｅ，ＷｕＢ…     

P—adic超越连分数

本文借助于Ｔｈｕｅ－Ｓｉｅｇｅｌ－Ｒｏｔｈ定理的Ｐ－ａｄｉｃ类似，Ｐ－ａｄｉｃ代数数的有理逼近定理以及Ｐ－ａｄｉｃ简单连分数的一些性质给出了Ｐ－ａｄｉｃ数是超越数的两个充分条件。     

Quantum thermal effect of quasi-static evaporating charged black hole

The study of quantum thermal effect of non-static black hole is generalized to the space-time with coordinate (t, r) as variables. Tortoise coordinate equations which are different from not only static space-time but also the non-static space-time described by advanced-Eddington coordinatev have been chosen. Under the condition that the effect of Hawking evaporation is considered, the temperature of black hole and the location of horizon are shown. The results indicate that Hawking radiation temperature can be regarded as a compensating effect under the time-scale transformation. Project supported by the National Natural Science Foundation of China.     

任意加速带电轴对称动态黑洞中Weyl中微子的热辐射

在任意加速带电动态轴对称时空中,采用新Tortoise坐标变换研究、Weyl中微子的量子热效应,得到事件视界的位置以及在视界面附近Weyl中微子的热辐射温度,导出Hawking热谱公式.结果表明视界的位置和辐射温度不仅随时间变化,而且依赖于角度.     

La radiation Hawking à l’horizon d’un trou noir

We establish the polarization of the quantum vacuum to a thermal state with the Hawking temperature, at the future black-hole horizon created by a gravitational collapse.     

基于Dirac方程研究双视界面黑洞的量子热效应和普朗克绝对熵

基于严格求解Dirac方程，全面研究了双视界面黑洞内、外视界附近的量子热效应，特别是考虑到黑洞内视界的Hawking吸收后，成功的给出了荷电黑洞的普朗克绝对熵。      

Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II

In this sequel paper, we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes that satisfy the dominant energy condition. We also include a third proof which builds on a known formula and describe a class of sufficient conditions of divergence type for the monotonicity of the Hawking mass. These flows of surfaces may have connections to the problem in general relativity of bounding the total mass of a spacetime from below by the quasi-local mass of spacelike 2-surfaces in the spacetime.     

Remarks on a Mean Field Equation on $\mathbb{S}^2$

In this note, we study symmetry of solutions of the elliptic equation\begin{equation*} -\Delta _{\mathbb{S}^{2}}u+3=e^{2u}\ \ \hbox{on}\ \ \mathbb{S}^{2},\end{equation*} that arises in the consideration of rigidity problem of Hawking mass in general relativity. We provide various conditions under which this equation has only constant solutions, and consequently imply the rigidity of Hawking mass for stable constant mean curvature (CMC) sphere.     

Regularity of inverse mean curvature flow in asymptotically hyperbolic manifolds with dimension 3

By using the nice behavior of the Hawking mass of the slices of a weak solution of inverse mean curvature flow in three-dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of the flow is star-shaped after a long time, and then we get the regularity of the weak solution of inverse mean curvature flow in asymptotically hyperbolic manifolds. As an application, we prove that the limit of the Hawking mass of the slices of a weak solution of inverse mean curvature flow with any connected C~2-smooth surface as initial data in asymptotically anti-de Sitter-Schwarzschild manifolds with positive mass is greater than or equal to the total mass, which is completely different from the situation in the asymptotically flat case.     

L'effet Hawking pour un champ de DiracThe Hawking effect for the Dirac field

We consider the gravitational collapse of the charged star leading to a black-hole. We prove that a fixed observer in Schwarzschild variables observes, at the last moments of the collapse in his own proper time, an outgoing thermal flux of spin 1/2 particles containing preferentially the particles with the same charge that the black-hole. This is the Hawking effect. To cite this article: F. Melnyk, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 643–648.