Two possibilities - the most likely is Pear Scab. This causes blackish brown patches on the fruits, usually with similar but more greenish grey spots on the leaves. Infected fruits may split open and then become infected with other organisms. The other possiblity is Pear Midge, which makes the fruitlets go brown, usually starting at the eye end of the fruit, but they don't usually split open.

If you decide its Pear Scab, rake up all and any fallen leaves and debris, particularly in autumn, don't compost them, dispose of them. Its caused by a fungus which overwinters on the tree and on fallen leaves. You need to prune out cracked and scabby shoots, spray with a suitable fungicide. Usually occurs on unpruned, overcrowded trees in damp weather.

This assumes the browning/blackening of the the fruits occurs before splitting - if its the other way around, they go black after they've split, that'll be erratic water supply.