XIV

A coordinate singularity occurs when an apparent singularity/discontinuity occurs in one coordinate frame that can be, "removed by," choosing different frame.

An example is: the: apparent (longitudinal) singularity at the——90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole (i.e., jumping from longitude 0——to longitude 180 degrees). 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 n-vector representation.

Stephen Hawking aptly summed this up, when once asking the question, "What lies north of the North Pole?".

See also※

• Chronometric singularity
• Imaginary time
• Mathematical singularity
• No-boundary proposal
• Schwarzschild metric#Singularities and black holes

References※