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).

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:

In Einstein's theory of general relativity, 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:

Kasner vacuum solution

In a Kaluza–Klein vacuum (static) field equations

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