The Wikipedia page about CieL*u*v* color space describes the conversion function from a color expressed in the XYZ color space.
For black, expressed as (R=0, G=0, B=0) in the RGB color space, and (X=0, Y=0, Z=0) in the XYZ color space, which values should we use to represent it in CieLuv?
The formula uses a division, 4x/(x+15y+3z), whose result is undefined for black.
Should we use (L=0, u=0, v=0), or are there more subtleties?
In fact black is not represented in uv. So in Luv black can be represented by L = 0 and u = v = undefined.