I don't see any black.
But I see a dead brown spot on the stem adjacent to where a side branch cracked off.

One or both stems may die.

Possibly Early Blight (Alternaria solani)

Try a copper & sulfer fungicide.

Thanks guys. I didn't try copper based fungicide, because I fear that may be poison to human. I tried Physan 20 (which was also being used on my orchids.) But the vine still died. The bright side is that the disease seems not spreading to my other tomatoes.