Electrovacuum Solution - Invariants

Invariants

As in flat spacetime, the electromagnetic field tensor is antisymmetric, with only two algebraically independent scalar invariants,

Using these, we can classify the possible electromagnetic fields as follows:

1. If but, we have an electrostatic field, which means that some observers will measure a static electric field, and no magnetic field.
2. If but, we have an magnetostatic field, which means that some observers will measure a static magnetic field, and no electric field.
3. If, the electromagnetic field is said to be null, and we have a null electrovacuum.

Null electrovacuums are associated with electromagnetic radiation. An electromagnetic field which is not null is called non-null, and then we have a non-null electrovacuum.