A fundamental assumption in the theory of brane world is that all matter and
radiation are confined on the four-dimensional brane and only gravitons can
propagate in the five-dimensional bulk spacetime. The brane world theory did
not provide an explanation for the existence of electromagnetic fields and the
origin of the electromagnetic field equation. In this paper, we propose a model
for explaining the existence of electromagnetic fields on a brane and deriving
the electromagnetic field equation. Similar to the case in Kaluza-Klein theory,
we find that electromagnetic fields and the electromagnetic field equation can
be derived from the five-dimensional Einstein field equation. However, the
derived electromagnetic field equation differs from the Maxwell equation by
containing a term with the electromagnetic potential vector coupled to the
spacetime curvature tensor. So it can be considered as generalization of the
Maxwell equation in a curved spacetime. The gravitational field equation on the
brane is also derived with the stress-energy tensor for electromagnetic fields
explicitly included and the Weyl tensor term explicitly expressed with matter
fields and their derivatives in the direction of the extra-dimension. The model
proposed in the paper can be regarded as unification of electromagnetic and
gravitational interactions in the framework of brane world theory.Comment: 8 page
