It's a mineral formation. tell tale in the formations on the crack. Path of least resistance for water thats getting under and evaporating out carring everything with it, The black could be coming from slate as well, as it is up steam from the drain.
If You can remove it, probably matter of time before it returns.
Get most of it on surface mechanically, razors or carbide tips or diamonds
Most will be on surface, however being unfilled trav, that black may be inside trav.
Last resort before replacement -try media blast or phosphric- then fill stone
Majority of roof
tops hard surface, balconies, I see are not built correct and alway a problem