Its not recommended to drink black coffee or any other coffee on an empty stomach because it can potentially cause damage to your stomachs lining and cause indigestion and heartburn.
What's recommended when drinking black coffee or any coffee is to eat some breakfast first to get something in your stomach and then drink your coffee along with the coffee.
That way your stomach won't be empty when you drink the coffee and won't potentially have those issues of the indigestion and heartburn as well as the potential damage to the stomach lining.
However sometimes I drink coffee on an empty stomach while fixing my breakfast and my stomachs been okay.
But if you suffer from indigestion or heartburn then it would be best to eat something first and then drink the coffee.
But you can drink the coffee on an empty stomach if you want too.