90° Shockley partial dislocations in GaN are investigated by first-principles calculations. This work is focussed on the electrical properties of dislocation cores, and on investigating the electrical fields around these defects. The band structure analysis shows that both the a and β core partials possess a midgap state. The β-core dislocations give rise to a donor level E-v + 0.87 eV that might explain the absorption peak at 2.4 eV revealed by energy loss spectroscopy measurements. The acceptor level E-v + 1.11 eV localized at the a-core dislocations might contribute to the yellow luminescence. These dislocations experience a substantial charge polarization along the [0001] growth axis. In addition, we show that these dislocations tend to charge in a high stress field.