Yes, time dilation occurs more prominently as we approach the center of the galaxy. According to Einstein's theory of general relativity, gravity affects the curvature of spacetime, which in turn influences the flow of time. In regions with stronger gravitational fields, such as near massive objects like black holes or the dense central region of a galaxy, time dilation becomes more pronounced.
The central region of a galaxy typically contains a supermassive black hole, which exerts a strong gravitational pull. As one approaches the center, the gravitational field becomes increasingly intense. This gravitational field causes time to pass more slowly relative to regions with weaker gravitational fields.
However, it's important to note that the degree of time dilation near the center of a galaxy depends on the specific distribution and concentration of mass. Additionally, factors such as velocity and proximity to other massive objects can also influence the observed time dilation.