Maxwell's equations in curved spacetime

In physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (where the metric may deviate from the Minkowski metric) or where one uses an arbitrary (not necessarily Cartesian) coordinate system. These equations can be viewed as a generalization of the vacuum Maxwell's equations which are normally formulated in the local coordinates of flat spacetime.

Source: Wikipedia — Maxwell's equations in curved spacetime (CC BY-SA 4.0)