This is necessary for consistency with the Einstein field equations.

The links between these forces are shown in the Einstein field equations.

This is just a question of similar choices, since for each chosen writing the Einstein field equations are the same.

The Einstein field equations are nonlinear and very difficult to solve.

There are relatively few exact solutions to the Einstein field equations.

The first term gives us what we need for the left-hand side of the Einstein field equations.

A common example of this method results in the linearised Einstein field equations.

Therefore, it is a solution of the Einstein field equations:

The Einstein field equations describe how this curvature is produced.

The expansion into a series gives a linearization of the Einstein field equations.

It is used in the Einstein field equations.

It is important to realize that the Einstein field equations alone are not enough to determine the evolution of a gravitational system in many cases.

Then one is able to solve the Einstein field equations as a series in , dropping higher order terms for simplicity.

This demonstrated the existence of exact radiating solutions to the Einstein field equations.

The Einstein field equations alone do not fully determine the evolution of the metric relative to the coordinate system.

This was the first solution to the Einstein field equations other than the trivial flat space solution.

These are exact vacuum solutions of the Einstein field equations with cylindrical symmetry.

There are practical as well as theoretical reasons for studying solutions of the Einstein field equations.

A description of physics including gravity governed by the Einstein field equations, i.e. full general relativity.

This was demonstrated by showing that solutions to the Einstein field equations diverge in a finite time.

The solutions of the Einstein field equations are metrics of spacetime.

These assumptions when applied to the Einstein field equations naturally result in a universe which has the following features:

The nonlinearity of the Einstein field equations often leads one to consider approximation methods in solving them.

The equations in contexts outside of general relativity are still referred to as the Einstein field equations.

From a purely mathematical viewpoint, it is interesting to know the set of solutions of the Einstein field equations.