# Vacuum solution

A vacuum solution is a solution of a field equation in which the sources of the field are taken to be identically zero. That is, such field equations are written without matter interaction (i.e.- set to zero).

## Examples

• In Maxwell's theory of electromagnetism, a vacuum solution would represent the electromagnetic field in a region of space where there are no electromagnetic sources (charges and electric currents), i.e. where the current 4-vector vanishes:[1]
$J^a=0$
• Einstein's theory of general relativity where a vacuum solution[2] would represent the gravitational field in a region of spacetime where there are no gravitational sources (masses), i.e. where the energy-momentum tensor vanishes:[3]
$T_{ab}=0$
• Kasner vacuum solution[5]