标题： 一类推广平衡解的爱因斯坦-麦克斯韦场 显示英文标题

标题： A Class of Einstein-Maxwell Fields Generalizing the Equilibrium Solutions

摘要： 爱因斯坦-麦克斯韦场的旋转静态源由满足\[ \nabla \cdot [\Theta ^{-1}(\Psi_A\nabla \Psi_B-\Psi_B\nabla \Psi_A)]=-2\Theta ^{-2}\vec{C}\cdot (\Psi_A\nabla \Psi_B-\Psi_B\nabla \Psi_A) \]的 SU(2,1) 旋量势$\Psi_A$表示，其中$\Theta =\Psi ^{\dagger }\cdot \Psi $是$\Psi $的 SU(2,1) 范数 % 。 厄恩斯特势通过旋量势用$% {\cal E}=\frac{\Psi_1-\Psi _2}{\Psi_1+\Psi_2}$，$\Phi =\frac{\Psi_3}{% \Psi_1+\Psi_2}$表示。 由源的旋转唯一生成的群不变向量$\vec{C}=-2i\func{Im}\{\Psi ^{\dagger}\cdot \nabla \Psi \}$，因此将$\vec{C}$称为场的{\em 旋涡}是合适的。 静态场没有涡流。 没有涡流的场是一类推广了爱因斯坦-麦克斯韦场的平衡（$| e| =m$）类。 我们为此类获得了可积性条件以及一组高度对称的场方程，以及精确解和一个开放的研究问题。 显示英文摘要

摘要： The Einstein-Maxwell fields of rotating stationary sources are represented by the SU(2,1) spinor potential $\Psi_A$ satisfying \[ \nabla \cdot [\Theta ^{-1}(\Psi_A\nabla \Psi_B-\Psi_B\nabla \Psi_A)]=-2\Theta ^{-2}\vec{C}\cdot (\Psi_A\nabla \Psi_B-\Psi_B\nabla \Psi_A) \] where $\Theta =\Psi ^{\dagger }\cdot \Psi $ is the SU(2,1) norm of $\Psi $% . The Ernst potentials are expressed in terms of the spinor potential by $% {\cal E}=\frac{\Psi_1-\Psi _2}{\Psi_1+\Psi_2}$, $\Phi =\frac{\Psi_3}{% \Psi_1+\Psi_2}$ . The group invariant vector $\vec{C}=-2i\func{Im}\{\Psi ^{\dagger}\cdot \nabla \Psi \}$ is generated exclusively by the rotation of the source, hence it is appropriate to refer to $\vec{C}$ as the {\em swirl} of the field. Static fields have no swirl. The fields with no swirl are a class generalizing the equilibrium ($| e| =m$) class of Einstein-Maxwell fields. We obtain the integrability conditions and a highly symmetrical set of field equations for this class, as well as exact solutions and an open research problem.