论文标题
充电球体及其稳定性的确切解决方案。 I.完美的液体
Exact solutions for charged spheres and their stability. I. Perfect Fluids
论文作者
论文摘要
我们研究了爱因斯坦 - 马克斯韦尔方程的确切溶液，用于静态球形对称带电球体的内部重力场。球体由完美的流体组成，其电荷分布会产生静态径向电场。流体的惯性质量密度具有$ρ（r）=ρ_O +αr^2 $（$ρ_O$和$α$是常数）的形式，并且在半径$ r $中具有$ q =βr^3 $（$β$是常数）的总收费$ q（r）$是一个常数。我们评估这些球体的$ m/r $的关键值作为$ q/r $的函数，并将这些值与Andréasson公式给出的值进行比较。
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres are composed of a perfect fluid with a charge distribution that creates a static radial electric field. The inertial mass density of the fluid has the form $ρ(r) = ρ_o + αr^2$ ($ρ_o$ and $α$ are constants) and the total charge $q(r)$ within a sphere of radius $r$ has the form $q = βr^3$ ($β$ is a constant). We evaluate the critical values of $M/R$ for these spheres as a function of $Q/R$ and compare these values with those given by the Andréasson formula.
