爱因斯坦场方程解的不变构造 - LRS 完美流体 I

examined in order to demonstrate the usage of the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives for finding solutions to Einstein's field equations. A new method is introduced, which makes it possible to choose the coordinates at any stage of the calculations. Three classes are examined, one with fluid rotation, one with spatial twist in the preferred direction and the space-time homogeneous models. It is also shown that there are no LRS space-times with dependence on one null coordinate. Using an extension of the method, we find the full metric in terms of curvature quantities for the first two classes.