Abstract
Considering Joule heating caused by the dissipation of the magnetic field in the neutron star crust to be an efficient mechanism in maintaining a relatively high surface temperature in very old neutron stars, the role of general relativity is investigated. It is found that, although the effect of space-time curvature produced by the intense gravitational field of the star slows down the decay rate of the magnetic field, modification of the initial magnetic field configuration and the initial field strength by the space-time curvature results in increasing the rate of Joule heating. Hence the space-time curvature supports Joule heating in maintaining a relatively high surface temperature which is consistent with the bservational detection.
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