|
Vacuum solutions of the Einstein field equations are those for which the Ricci tensor is zero in a given region of spacetime, i.e.,
<math>R_{ab}=0<math>
In this region, the Riemann and Weyl tensors are equal; hence,
<math>R_{abcd}=C_{abcd}<math>
Note that for a vacuum solution of the field equations (with <math>\Lambda =0<math>), the energy-momentum tensor is zero:
<math>T_{ab}=0<math>
The most famous vacuum solution is the (exterior) Schwarzschild solution, which can be used to model the spacetime geometry in the vicinity of a star.
|
