My broken tooth is black inside, is it tooth decay or something else?

You need to check with your dentist ASAP because it could be as simple as cavity to pulpal infection(nerve infection) . Your dentist can determine exactly what will be right solution for you. Best of luck

Hello and thank you for your question. I would advise you to see a dentist asap, BEFORE it starts hurting. 
Most likely it is a decay, possible, a silver filling, which got dark over the years. In either case, broken tooth should be fixed. Otherwise, there is a huge risk of tooth lose.
All the best to you!

It could be decay, it could be discoloration from an old silver filling or could result from a long term pulp issue. The only way to find out is to see a dentist promptly and have it checked. If you don't see a dentist and have it treated though, it will get worse no matter what the cause.