# 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

### Maxwell's equations

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[clarification needed] 4-vector vanishes:[1]

${\displaystyle J^{a}=0}$

### Einstein field equations

In Einstein's theory of general relativity, 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]

${\displaystyle T_{ab}=0}$

#### Kasner space

Kasner vacuum solution[4]

### Kaluza–Klein theory

In a Kaluza–Klein vacuum (static) field equations[5]