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:

$J^a=0$

• Einstein's theory of general relativity where a vacuum solution 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:

$T_{ab}=0$

• Kaluza–Klein vacuum (static) field equations

• Kasner vacuum solution

See also

• Einstein field equations
• Kasner metric
• Kerr metric
• Maxwell's equations
• Vacuum solution (general relativity)