Cauchy’s Problem for Einstein’s Equations

Abstract

There are two complementary ways to use Einstein’s equations:

$$\begin{aligned} G_{\alpha \beta } = -\chi \, T_{\alpha \beta }. \end{aligned}$$

After choosing a momentum–energy tensor on the basis of some physical assumptions, we can try to determine the solutions of Einstein’s equations corresponding to that momentum–energy tensor. For example, if the momentum–energy tensor of a perfect fluid is chosen and a spherically symmetric solution is searched for, then a reasonable stellar model is obtained.