Vacuum solution

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A vacuum solution is a solution of a field equation in which the sources of the field are taken to be identically zero.

For example, 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

Another example is 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