Coordinate singularity
A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame that can be removed by choosing a different frame.
An example is the apparent singularity at the 90 degree latitude in spherical coordinates. An object moving due north on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole. In fact, longitude is not uniquely defined at the poles. This discontinuity, however, is only apparent; it is an artifact of the coordinate system chosen, which is singular at the poles. A different coordinate system would eliminate the apparent discontinuity, e.g. by replacing the latitude/longitude representation with an -vector representation.
Stephen Hawking aptly summed this up, when once asking the question, "What lies north of the North Pole?".
