共形球(平面)对称的电磁真空解必为Reissner-Nordstrom(Kar)度规

本文推广了广义相对论的两个定理, 把定理条件中的对称性减弱为共形对称性.推广后的定理为: l)Einstein 方程的共形球对称电磁真空解必为Reissoer-Nordsorom 解; 2 ))Einstein 方程的共形平面对称电磁真空解必为Kar 解. 关键词：     

LU(1)群的引力规范场球对称静态解

寻找引力规范理论场方程的严格解要比寻找Einstein场方程的严格解更为困难。但是,对某些物理问题来说,能够求得牛顿型近似解和后牛顿型的近似解就足够了。本文研究了一种Lorentz群和U(1)群为规范群的引力规范理论,求得了带电粒子的球对称静场的特殊有挠解,并求得了有挠的一阶近似解。     

《从零学相对论》连载(19)

正第8讲史瓦西时空§8.1史瓦西真空解史瓦西真空解是爱因斯坦方程的第一个精确解(§6.5),描述一个静态的、球对称的物质分布(通常是天体)在其外部(真空区域)造成的时空弯曲,这一弯曲线元可用史瓦西坐标系{t,r,θ,φ}表为     

L?(1)群的引力规范场球对称静态解

寻找引力规范理论场方程的严格解要比寻找Einstein场方程的严格解更为困难。但是,对某些物理问题来说,能够求得牛顿型近似解和后牛顿型的近似解就足够了。本文研究了一种Lorentz群和U(1)群为规范群的引力规范理论,求得了带电粒子的球对称静场的特殊有挠解,并求得了有挠的一阶近似解。 关键词：     

柱对称Einstein方程的可积性和几何意义

本文采用规范协变形式讨论了柱对称Einstein方程, 将其基本方程与对称空间中相应的孤子面的第一, 第二微分基本形式相联系, 利用体系的对偶对称性给出了线性散射方程, Bäcklund变换和Ricati方程, 讲明了它们的可积性, 得到了相应的几何解释.     

《从零学相对论》连载26

正§8.8伯克霍夫定理正如§6.5所云,史瓦西之所以能够很快就求得真空爱因斯坦方程的第一个精确解,是因为他巧妙地利用了问题本身的对称性——恒星既是球对称的,又是静态的.然而,任何恒星都不是永恒不变的,它们也像人一样要经历生、老、病、死等各个演化阶段,恒星在许多阶段中并不处于静态之中,这时恒星外部的时空几何还可用史瓦西真空线元式(8-7-1)描述吗?如果有人向史瓦西提出这个问题,恐怕     

对称张量场共形协变方程的真空解

本文讨论了对称张量场共形协变方程的真空解.     

完整系统Appell方程Mei对称性的共形不变性与守恒量

研究完整系统Appell方程Mei对称性的共形不变性与守恒量. 引入无限小单参数变换群及其生成元向量, 定义完整系统动力学方程的Mei对称性和共形不变性, 给出该系统Mei对称性共形不变性的确定方程. 利用规范函数满足的结构方程导出系统相应的Mei守恒量. 举例说明结果的应用. 关键词： Appell方程 Mei对称性 共形不变性 Mei守恒量     

相对运动完整系统Appell方程Mei对称性的共形不变性与守恒量

研究相对运动完整系统Appell方程Mei对称性的共形不变性与守恒量. 引入无限小单参数变换群及其生成元向量, 给出相对运动完整系统Appell方程的Mei对称性和共形不变性的定义, 导出系统Mei对称性的共形不变性确定方程, 重点讨论系统共形不变性和Mei对称性的关系, 然后借助规范函数满足的结构方程导出系统Mei对称性导致的Mei守恒量表达式, 最后举例说明结果的应用.     

共形协变非线性耦合方程的真空解

我们讨论了标量-旋量共形协变非线性耦合方程的instantonlike和meronlike真空解.     

Non-Existence of Multiple-Black-Hole Solutions Close to Kerr–Newman

We show that a stationary asymptotically flat electro-vacuum solution of Einstein’s equations that is everywhere locally “almost isometric” to a Kerr–Newman solution cannot admit more than one event horizon. Axial symmetry is not assumed. In particular this implies that the assumption of a single event horizon in Alexakis–Ionescu–Klainerman’s proof of perturbative uniqueness of Kerr black holes is in fact unnecessary.     

Self-gravitating scalar field with cubic nonlinearity

For a self-gravitating massless conformally invariant scalar field a solution is obtained to the Einstein equations for which the geometry of space-time remains arbitrary. For a scalar field with cubic nonlinearity, a static solution to the Einstein equations possessing plane symmetry is found. A cosmological model with nonlinear scalar field in the class of conformally flat Friedmann metrics is investigated. An example is given of an exact solution to the equations of the gravitational field with singularity in the infinite past.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 18–22, December, 1980.     

Stationary vacuum fields with a conformally flat three-space. II. Proof of axial symmetry

The conjecture is proved that stationary vacuum space-times having a conformally flat three-space are axially symmetric. The proof uses the Ernst potential and the complex conjugate potential as independent coordinates. Two field equations: a combination of the Einstein equations and an integrability condition are algebraic in one of the field variables. Their coefficients, computed by employing a REDUCE program, separately vanish unless axial symmetry holds. Solution of the coefficient equations yields the proof of axial symmetry. Certain special classes of metrics must be excluded from the discussion. The axial symmetry of these exceptional classes has been proved in I.     

双荷静止球对称天体Einstein-Maxwell方程的共形平直内解

严格解出了一种既荷电又荷磁，且电荷密度与磁荷密度之比为常量的静止球对称天体的共形平直内解．     

Generating conjecture and Einstein-Maxwel field of plane symmetry

For the plane symmetry we have found the electro-vacuum exact solutions of the Einstein-Maxwell equations and we have shown that one of them is equivalent to the McVittie solution of a charged infinite thin plane. The analytical extension has been accomplished and the Penrose conformal diagram has been obtained as well.     

Conformally planar gravitational fields produced by matter

A geometric property (spherical symmetry) which unambiguously distinguishes homogeneous cosmological models (Friedmann spaces) from other conformally planar gravitational fields is pointed out. Certain general properties of the distribution and motion of matter in conformally planar gravitational fields are established, and new solutions of the Einstein equations are derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 67–73, November, 1969.The author thanks D. D. Ivanenko and the participants in a seminar under his guidance for discussion of these results.     

Do semiclassical zero temperature black holes exist?

The semiclassical Einstein equations are solved to first order in epsilon = Planck's over 2pi/M2 for the case of a Reissner-Nordstr?m black hole perturbed by the vacuum stress energy of quantized free fields. Massless and massive fields of spin 0, 1/2, and 1 are considered. We show that in all physically realistic cases, macroscopic zero temperature black hole solutions do not exist. Any static zero temperature semiclassical black hole solutions must then be microscopic and isolated in the space of solutions; they do not join smoothly onto the classical extreme Reissner-Nordstr?m solution as epsilon-->0.     

Gravity/CFT correspondence for three-dimensional Einstein gravity with a conformal scalar field

We study the three-dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an infinite Newton?s constant. There is a class of solutions with possible curvature singularities which asymptotic symmetries are given by two copies of the Virasoro algebra. We argue that the central charge of the corresponding CFT is infinite. Furthermore, we construct a family of Schwarzschild solutions which can be conformally mapped to the Martínez–Zanelli solution of Einstein?s equations with a negative cosmological constant coupled to conformal scalar field.     

Invariant solutions and conservation laws of Einstein field equations in non-comoving radiation fields

The exact non-static accelerating solutions of Einstein field equations in non-comoving pure radiation fields, corresponding to an indefinite non-degenerate metric in cartesian coordinates, are obtained. The gravitational field is of Petrov type $D$ and the considered spacetime is not conformally flat. Lie symmetry method is used for symmetry reduction of nonlinear partial differential equations and for finding the exact solutions, comprising both arbitrary functions and known analytic functions. Conservation laws are obtained by using multiplier approach. The graphical representations of solutions are shown by considering different possibilities of the arbitrary functions.