Answer: There are different instances of arborvitae foliage turning black and looking like tar as you are describing. Some of what you see, the browning at the interior, may be normal since they lose some foliage each spring in this way. The blackening is not normal, and could be caused by a variety of reasons. In some cases pet urine does cause it, as could contact with fertilizer salts such as through accidental overspread from a cyclone style spreader.
There is also a possibility of sooty mold growing on damage sites from scale insect injury, but in other cases it seems to be a combination of environmental factors that are not well understood, perhaps due to sudden temperature shifts (we have had those this spring for sure!), perhaps excess humidity, perhaps a lack of air circulation, but not always something we can really account for. In most cases the plant's overall health seems to be unaffected although it is a bit unsightly -- since your plants seem to be doing well I would expect it to be in the "nothing serious just ugly group". To be sure, though, you might want to take a sample and maybe a photo to your county extension and/or consult with a licensed, certified professional arborist about it to make sure that it is nothing serious, and see if they have any suggestions as to what steps to take. I'm sorry I can't be more specific long distance.
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