Black finger tips indicate that dead blood has accumulated at the finger tips. The tissue at the finger tips are dying or have died.
soak the finger tips in warm or hot water. Then massage the finger tips. Try to invigorate blood flow and oxygen flow to the finger tips.
Exercise the fingers and hands by shaking the hands and making fists with the fingers. Do these exercises and soak the finger tips in hot water every hour or two until the accumulation of dead blood goes away.
The consequence of not taking care of the finger tips immediately is amputation of the fingers.