As the time it takes for a white dwarf to cool down and become a black dwarf is so long, there is little chance that any have formed in the observable Universe; there has not been enough time the big bang. 

Black dwarfs should not be confused with brown dwarfs, which are essentially "failed" stars.  They have masses in the range from approximately 13 times Jupiter's mass, up to perhaps 75 to 80 times Jupiter's mass, and do not support hydrogen burning nuclear fusion. 


Black dwarf stars are the hypothetical remnant of a white dwarf that has cooled down to where it no longer radiates; no heat, no light.  Stars that start off with from .075 solar masses up to around 4 solar masses become white dwarfs; essentially a ball of electron-degenerate matter, slowly cooling.  Larger stars, up to even 10 solar masses, can produce white dwarfs if they looses sufficient mass during their lives.  A white dwarf is very small, perhaps the size of the Earth, with a small surface area, so the cooling process proceeds very slowly.  Estimates of the time required to form a black dwarf vary widely from 2.5x1010 to 1x1012 years.  There are various theoretical ways in which this time could be even longer:

Black Dwarfs

Astronomy & Cosmology -

Stars - Life & Death of Stars

WILLIAM & DEBORAH HILLYARDWILLIAM & DEBORAH HILLYARD

If Dark Matter is found to include weakly interacting massive particles (WIMPs), it is possible that interactions between the star and WIMPs could extend the time to as much as 1025 years. 

If protons are found to decay, theorized in some Grand Unified Theories to happen over a period of perhaps 1036 years, then this process would also keep the star slightly warm, but only marginally above absolute zero. 
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