The Einstein field equations (EFE) may be written in the form:
$${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }}$$
where See more

If the energy–momentum tensor Tμν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor
Additionally, the See more

The nonlinearity of the EFE makes finding exact solutions difficult. One way of solving the field equations is to make an approximation, namely, that far from the source(s) of gravitating matter, the gravitational field is very weak and the spacetime See more

In the Einstein field equations
• any desired steady state solution described by this equation is unstable, and
• observations … See more

If the energy–momentum tensor Tμν is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations. By setting Tμν = 0 in the … See more

The solutions of the Einstein field equations are metrics of spacetime. These metrics describe the structure of the spacetime including the inertial motion of objects in the … See more

Despite the EFE as written containing the inverse of the metric tensor, they can be arranged in a form that contains the metric tensor in … See more