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Considering Joule heating caused by the dissipation of the magnetic field inthe neutron star crust to be an efficient mechanism in maintaining a relativelyhigh surface temperature in very old neutron stars, the role of generalrelativity is investigated. It is found that, although the effect of space-timecurvature produced by the intense gravitational field of the star slows downthe decay rate of the magnetic field, modification of the initial magneticfield configuration and the initial field strength by the space-time curvatureresults in increasing the rate of Joule heating. Hence the space-time curvaturesupports Joule heating in maintaining a relatively high surface temperaturewhich is consistent with the bservational detection.Comment: 10 pages, Latex (aaspp4 style), 8 postscript figures, Sheduled to  appear in the 20th Nov. 2000 issue of the Astrophysical Journa

Joule Heating in Neutron Stars under Strong Gravitation