Bored and don't have a clue,but I googled it and found this:

Here is a link that might be useful: cleaning soot from stone

Just do not use a steel wire brush.

Steel metal will smear on the stone and then slowly cause rust to appear.

Brass or plastic brushes.

The more often you clean up, the less dusty it will be......

I saw on HGTV that you can use oven cleaner and a scrub brush and it will do the trick. Make sure to take all safety precautions glasses, mask, and cover your skin. I do not know if this works just passing along the tip!

Good luck,
Red