Black "ghosting" on the walls

[Clayton Swansen]

Hello everyone! Well, I recently made the plunge into the world of REI with big thanks to Bigger Pockets, and my local investors group. I am extremely excited, and nervous about my new life as a landlord. I have already dealt with a few small challenges, but this one I felt the need to bring to the BP forum...

One of the units in my triplex has this black stuff all over the walls. It looks like soot. I thought it was from burning candles, but the tenant does not burn many. She has been in the unit for 22 years, and has no idea where it could be coming from. She had it tested, and it is not black mold. It seems worst directly above the baseboard heaters, so my thought is that the heaters are burning dust when they are on. Does anyone have any experience here? Any good advice?

Your help is greatly appreciated. Thanks, BP!