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 charges and electric currents, i.e. where the current 4-vector vanishes: Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...
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Another example would be in Einstein's theory of general relativity where a vacuum solution would represent the gravitational field in a region of spacetime where there are no masses, i.e. where the energy-momentum tensor vanishes: Two-dimensional visualisation of space-time distortion. ...
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