标题： 静态爱因斯坦方程的基本解与相对论引力中的叠加原理 显示英文标题

标题： Static Fundamental Solutions of Einstein Equations and Superposition Principle in Relativistic Gravityv

摘要： 我们证明爱因斯坦方程与存在质量点粒子理想化模型是相容的，并找到了相应的两参数解族。 它们由裸机械质量$M>0$和点源的开普勒质量$m>0$($m < M$) 完全定义。 这些解在复平面上的全局解析性质定义了单粒子问题的一个优选径向变量。 这些新解是准线性爱因斯坦方程的基本解。 我们引入并讨论了爱因斯坦方程解的新非线性叠加原理，并发现了相对论性牛顿引力势的类比的基本作用。 对于相对论势，我们引入了一个简单的准线性叠加原理作为爱因斯坦方程初始条件的新物理要求，从而证明了N粒子系统的瞬时重力静止情况。 这个叠加原理使我们能够勾勒出一种新的引力质量缺陷理论。 其中，开普勒质量$m$的特定马赫类似原理成立，即它依赖于宇宙中的质量分布，与保持为真正常数的裸质量$M$相反。 考虑了几种离散和连续质量分布的基本例子。 显示英文摘要

摘要： We show that Einstein equations are compatible with the presence of massive point particle idealization and find the corresponding two parameter family of solutions. They are complete defined by the bare mechanical mass $M>0$ and the Keplerian mass $m>0$ ($m < M$) of the point source of gravity. The global analytical properties of these solutions in the complex plane define a unique preferable radial variable of the one particle problem. These new solutions are fundamental solutions of the quasi-linear Einstein equations. We introduce and discuss a novel nonlinear superposition principle for solutions of Einstein equations and discover the basic role of the relativistic analog of the Newton gravitational potential. For the relativistic potential we introduce a simple quasi-linear superposition principle as a new physical requirement for the initial conditions for Einstein equations, thus justifying the instant gravistatic case for N particle system. This superposition principle allows us to sketch a new theory of the gravitational mass defect. In it a specific Mach-like principle for the Keplerian mass $m$ is valid, i.e. it depends on the mass distribution in the universe, in contrast to the bare mass $M$, which remains a true constant. Several basic examples both of discrete and of continuous mass distributions are considered.