  The space-time curvature carried by electromagnetic fields is discovered and
a new unification of geometry and electromagnetism is found. Curvature is
invariant under charge reversal symmetry. Electromagnetic field equations are
examined with De Rham co homology theory. Radiative electromagnetic fields must
be exact and co exact to preclude unobserved massless topological charges.
Weyl's conformal tensor, here called ``the gravitational field'', is decomposed
into a divergence-free non-local piece with support everywhere and a local
piece with the same support as the matter. By tuning a local gravitational
field to a Maxwell field the electromagnetic field's local gravitational field
is discovered. This gravitational field carries the electromagnetic field's
polarization or phase information, unlike Maxwell's stress-energy tensor. The
unification assumes Einstein's equations and derives Maxwell's equations from
curvature assumptions. Gravity forbids magnetic monopoles! This unification is
stronger than the Einstein-Maxwell equations alone, as those equations must
produce the electromagnetic field's local gravitational field and not just any
conformal tensor. Charged black holes are examples. Curvature of radiative null
electromagnetic fields is characterized.
