In regions where the gravitational forces cancel out, such as at the Earth's core or any point within a uniform gravitational field, the effects of time dilation become negligible. Time dilation is directly influenced by the strength of the gravitational field experienced by an object.
In general relativity, the gravitational time dilation is described by the equation:
Δt' = Δt * sqrt(1 - (2GM)/(c^2r))
where Δt' is the time interval experienced by an observer in a gravitational field, Δt is the time interval measured by a distant observer (far from the gravitational field), G is the gravitational constant, M is the mass causing the gravitational field, c is the speed of light, and r is the distance from the center of the gravitational field.
As you approach the Earth's core, the distance from the center of the gravitational field decreases (r approaches zero), but the mass causing the gravitational field (M) also decreases since you are getting closer to the center. As a result, the gravitational time dilation factor approaches unity, indicating that time dilation becomes negligible in these regions.
Therefore, in the Earth's core or any other region where the gravitational forces cancel out, the effects of time dilation by gravity can be considered minimal or effectively canceled out.