  An analysis of the role of general relativistic effects on the decay of
neutron star's magnetic field is presented. At first, a generalized induction
equation on an arbitrary static background geometry has been derived and,
secondly, by a combination of analytical and numerical techniques, a comparison
of the time scales for the decay of an initial dipole magnetic field in flat
and curved spacetime is discussed. For the case of very simple neutron star
models, rotation not accounted for and in the absence of cooling effects, we
find that the inclusion of general relativistic effects result, on the average,
in an enlargement of the decay time of the field in comparison to the flat
spacetime case. Via numerical techniques we show that, the enlargement factor
depends upon the dimensionless compactness ratio ${\epsilon}={2GM \over
c^{2}R}$, and for ${\epsilon}$ in the range $(0.3~,~0.5)$, corresponding to
compactness ratio of realistic neutron star models, this factor is between 1.2
to 1.3. The present analysis shows that general relativistic effects on the
magnetic field decay ought to be examined more carefully than hitherto. A brief
discussion of our findings on the impact of neutron stars physics is also
presented.
