Electrovacuum solution

In general relativity, an electrovacuum solution (electrovacuum) is an exact solution of the Einstein field equation in which the only nongravitational mass-energy present is the field energy of an electromagnetic field, which must satisfy the (curved-spacetime) source-free Maxwell equations appropriate to the given geometry. For this reason, electrovacuums are sometimes called (source-free) Einstein-Maxwell solutions.

In general relativity, the geometric setting for physical phenomena is a Lorentzian manifold, which is physically interpreted as a curved spacetime, and which is mathematically specified by defining a metric tensor ${\displaystyle \,g_{ab}}$ (or by defining a frame field). The Riemann curvature tensor ${\displaystyle \,R_{abcd}}$ of this manifold and associated quantities such as the Einstein tensor ${\displaystyle G^{ab}}$, are mathematically well-defined. In general relativity, they can be interpreted as geometric manifestations (curvature and forces) of the gravitational field.

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