We present the solution of the Einstein field equations, in the static and spherically symmetric case, for an incompressible fluid, that has constant proper energy density at each and every point of the volume where it exists, according to a set of local observers who are stationary with respect to the fluid at each point. In the general case the fluid exists within a spherically symmetric shell with an inner vacuum-matter interface at a radial position \(r_{1}\) and an outer matter-vacuum interface at a radial position \(r_{2}\) in the Schwarzschild coordinate system. Therefore, in the general case there is an inner vacuum region with a repulsive singularity at the origin, just like in all other similar shell solutions. We present the parameter plane of the problem, and show that there are limits of solutions that approach the configuration of black holes, with the formation of an event horizon at the radial position \(r_{2}\).

根据一组当地观察者的说法，在静态和球对称情况下，我们提出了不可压缩流体的爱因斯坦场方程的解，该流体在其存在的体积的每个点上都具有恒定的适当能量密度。各点相对于流体静止。一般情况下，流体存在于球对称壳内，在径向位置 \(r_{1}\) 处具有内部真空-物质界面，在径向位置 \(r_{2}\) 处具有外部物质-真空界面在史瓦西坐标系中。因此，在一般情况下，就像所有其他类似的壳解一样，在原点处存在一个具有排斥奇点的内部真空区域。我们提出了问题的参数平面，并表明接近黑洞结构的解决方案存在局限性，在径向位置 \(r_{2}\) 处形成事件视界。