Certified GKH Gardening Expert
Oh no! This sounds like Black Heart Rot! This is terrible news.
There is no treatment, or cure. In fact, not much is known about the disease, other than it is an Alternaria fungus.
Simply, removing old fruit should help out for next year, but you will expect to see more infected next year. Using a fungicide may help some, but you won't rid yourself completely of the disease.
This article will help you understand what is happening to your tree: https://www.gardeningknowhow.com/edible/fruits/pomegranate/black-seeds-in-pomegranate.htm
this article will help you with fungicide use: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm