What's about "conurbation"?A town centre = the centre of a town.
A city centre = the centre of a city.
A centre of population = a location where there is a concentration of people who are resident.
An urban centre = a centre of population which is urban in nature.
You seem not to have understood the difference between centre and area. A centre is the middle of something, an area (in this context) is the whole thing.So, does it a good synonym of "urban centers"?