Pulsar glitches are commonly interpreted as angular momentum transfers occurring between two fluids present in the stellar interior, triggered by the rapid motion of superfluid vortex lines at large scales. We consider for the first time all general relativistic effects in a numerical model for glitches. First, we show numerical calculation of stationary configurations of neutron stars composed of a neutron superfluid and a fluid made of charged particles, spinning with different rotation rates. These general relativistic calculations are based on realistic equations of state accounting for entrainment effects between the fluids. These configurations are then used to build a numerical model for pulsar glitches in full general relativity. In particular, we study in details the characteristic time scale associated with the spin-up stage, during which the stellar dynamics are governed by a mutual friction force arising from the interactions between the superfluid vortices and the surrounding fluids. Taking general relativity into account leads to an additional coupling between the fluids through frame-dragging effects and is shown to affect significantly the actual value of the spin-up time scale.
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