I'm assuming that some time after the introduction of Christianity, slavery ceased. When and how did it happen and what were the consequences? Could the Byzantines likely have fared better against their enemies if they had kept using slaves?
You might want to re-think your assumption, as there's nothing inherently unchristian about slavery (the European colonial powers were all officially Christian, and all made use of slaves at some point). The Byzantines never abolished slavery, and were in fact very good customers for Russian slave-traders in the 12th century.
Byzantine slavery is a recognized phenomenon to the point that it is the subject of a book: Byzantine Slavery and the Mediterranean World (2009), by Youval Rotman. If you're interested in delving deeper into the topic, it's a good source.