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Vortex-mediated mutual friction governs the coupling between the superfluidand normal components in neutron star interiors. By, for example, comparingprecise timing observations of pulsar glitches with theoretical predictions itis possible to constrain the physics in the interior of the star, but to do soan accurate model of the mutual friction coupling in general relativity isneeded. We derive such a model directly from Carter's multifluid formalism, andstudy the vortex structure and coupling time-scale between the components in arelativistic star. We calculate how general relativity modifies the shape andthe density of the quantized vortices and show that, in the quasi-Schwarzschildcoordinates, they can be approximated as straight lines for realistic neutronstar configurations. Finally, we present a simple universal formula (given as afunction of the stellar compactness alone) for the relativistic correction tothe glitch rise-time, which is valid under the assumption that the superfluidreservoir is in a thin shell in the crust or in the outer core. This universalrelation can be easily employed to correct, a posteriori, any Newtonianestimate for the coupling time-scale, without any additional computationalexpense.

A universal formula for the relativistic correction to the mutual friction coupling time-scale in neutron stars