  Graviton-photon conversions in a given external electric or magnetic field,
known as the Gertsenshtein mechanism, are usually treated using the
four-potential for photons. In terms of the electric and magnetic (EM) fields,
however, proper identification of the fields in curved spacetime is important.
By misidentifying the fields in Minkowski form, as is often practiced in the
literature, we show that the final equation for photon conversion is correct in
transverse-tracefree gauge only for planar gravitational waves in a uniform and
constant external field. Even in the former method, to recover the EM fields
from the four-potential in curved spacetime, one should properly take into
account the metric involved in the relation. By including the metric
perturbation in the graviton conversion equation, we show that a magnetic
environment can cause tachyonic instability term in gravitational wave
equation.
