In general relativity (GR), the gravitational potential is indeed present at every point in space. The gravitational potential is associated with the curvature of spacetime caused by the presence of mass and energy. It affects the motion of all objects, including electromagnetic (EM) radiation.
However, when we talk about an electromagnetic potential, it refers to the vector potential (A) and scalar potential (Φ) in classical electromagnetism, which are used to describe the electromagnetic field. These potentials are not present at every point in space, but rather in regions where there is a changing electromagnetic field.
The reason for this distinction lies in the nature of the forces involved. The gravitational force, as described by GR, is a geometric property of spacetime curvature caused by mass and energy. It acts on all objects, including light, regardless of whether there is a changing gravitational field or not. The gravitational potential is always present and affects the motion of all particles and fields.
On the other hand, the electromagnetic force is associated with the interaction of charged particles and the electromagnetic field. The electromagnetic potential is related to this field, and it only exists in regions where there are changing electromagnetic fields. In other words, the electromagnetic potential arises due to the presence of charges or changing currents, which generate electromagnetic fields.
In summary, the gravitational potential exists at every point in space because it is associated with the curvature of spacetime caused by mass and energy. On the other hand, the electromagnetic potential is present only in regions where there are changing electromagnetic fields, such as where light is propagating or in the vicinity of charged particles or currents.