I find the similarities between the black arrow and Gurthang very big to be a coincidence. I believe that the sword and the arrow used to kill two of the most famous dragons where actually made of the same material.
The top of a dragon is suposed to be hard as mithril and its underside is descrived as "weaker" and mithril is one if not the strongest materials in Arda, so a dragons underside could still be very strong. I believe that if a dragon`s underside was made of thin and weak skin then Smaug would have been killed while attacking Dale because he did not have his "precious coat" and he certanly took many arrows, even maybe in the region where he would then be pierced by the black arrow, so we can guess that his underside can be as strong as iron... for one arrow to penetrate it as deeply as the black arrow did then it must be made of something very strong and sharp... mithril or something else. We now that mithril is silver/white in colour so we can rule out that idea, the only other psossibilitie is the metheorite from which the black swords Angachel/Gurthang and Anguirel.
We also an also especulate that the black arrow had some magic/will in it as Bard said that it has never failed him and that he had alwais recovered it, and we can be sure that the sword Gurthang had some sort of will as it spoke to Turin and broke when it killed him so we could think that this metal caught a part of the spirit of the smith that worked on it.
Eol was a friend of the dwarves so he coud have donnated some of his sky ore to his dwarven friends. They might have in turn exchanged part of the black metal for mithril with Durins Folk. Then when the balrog took Moria they might have rescued a small portion of the metal. Many years after it Thror could have used a portion to forge the arrow and give it as a friendship gift to Girion Lord of Dale.
What do you think? could this two black dragonslaying weapons have any relation with each other?