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\begin{equation}  G_{\mu\nu}+ \Lambda g_{\mu\nu}=\frac{8 \pi G}{c^4}T_{\mu\nu}  \end{equation}  These field equations are nonlinear and very difficult to solve. Given a specified distribution of matter and energy in the form of a stress–energy tensor, the EFE are understood to be equations for the metric tensor, as both the Ricci tensor and scalar curvature depend on the metric in a complicated nonlinear manner. In fact, when fully written out, the EFE are a system of 10 coupled, nonlinear, hyperbolic-elliptic partial differential equations.