# Equation for effects of the density on time dilation

The higher the density of an object is the more it will cause distortion on space and time.

I want to know the equation that links density to time dilation.

I found the Lorentz equations that link speed with time dilation but I cannot find the equations that does it for gravity...

Any help?

• There isn't one. Commented Sep 6, 2020 at 15:05
• Is it because there is just not one yet or am I wrong in my understanding of the General relativity? Commented Sep 6, 2020 at 15:08
• The problem is much harder to solve than you seem to think, so the latter. en.wikipedia.org/wiki/… Commented Sep 6, 2020 at 15:27
• didn't know it was that hard before your first message nut that was what I implied by "there is just not one yet". doesn't help my issue but it does help for my general knowledge... thank you Commented Sep 6, 2020 at 15:32
• OK in that case my first comment stands. Commented Sep 6, 2020 at 15:47

The density determines the curvature by the Einstein field equations: $$R_{\mu \nu} - \tfrac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu},$$ where $$R_{\mu \nu}$$ is a curvature tensor built up from derivatives of $$g_{\mu \nu}$$ and $$R=R^\mu{}_\mu.$$
The density however doesn't directly determine the gravitational time dilation. That can instead be determined from an actual solution $$g_{\mu \nu} = \phi(x) \, dt^2 - (\text{spatial distance})$$ by taking ratios of $$\phi(x)$$ for different positions.