It's any time you want! All the time zones come together at both poles, so asking what time it is at the North Pole is like asking which way is north.
Local time at all other locations on the Earth's surface is based on the Sun's position relative to the celestial meridian, an imaginary line running north and south directly
overhead. Noon is based on when the Sun crosses the local meridian, which also corresponds to its highest point in the sky on a given day.
At the North Pole, there is no north/south line that can define a meridian. Also, on any given day the Sun circles the sky at the same apparent altitude. There is no "highest position" to define noon.
By convention, I assume it would be convenient to select the prime meridian and its corresponding zulu time as the standard time at either pole.
Answered by:
Paul Walorski, B.A., Part Time Physics Instructor
'In a way science is a key to the gates of heaven, and the same key opens the gates of hell, and we do not have any instructions as to which is which gate.
Shall we throw away the key and never have a way to enter the gates of heaven? Or shall we struggle with the problem of which is the best way to use the key?'