The presence of a threading edge dislocation terminated at the surface of GaN bulk substrates causes a dipole-like strain state ranging over a several micrometer square area. The local strain state is derived from microphotoluminescence mappings of the near-band-edge spectrum and is quantitatively reproduced by a three-dimensional elastic deformation model approach. These results are compared with the local electrical potential distortion due to the core charge and attracted defects as analyzed by scanning surface-potential microscopy. In contrast to the local strain, the potential profile does not show a dipole-like behavior and decreases laterally faster.