Metric Tensor (general Relativity) - Einstein's Equations

Einstein's Equations

One of the core ideas of general relativity is that the metric (and the associated geometry of spacetime) is determined by the matter and energy content of spacetime. Einstein's field equations:

where

relate the metric (and the associated curvature tensors) to the stress-energy tensor . This tensor equation is a complicated set of nonlinear partial differential equations for the metric components. Exact solutions of Einstein's field equations are very difficult to find.