# Does a massive spherical shell expand the time inside itself?

The solution to your question is time A = time B < time C.

The reason is that since there is no mass inside the hollow region, the Schwarzschild radius is zero.

The metric in the hollow region is flat Minkowski space.

Time ticks still differently inside the shell then outside the shell.

Because where $$\Phi$$ is the gravitational potential, defined such that $$\Phi \to 0$$ as $$r \to \infty$$. Thus, $$d \tau = \sqrt{ 1 + \frac{2 \Phi}{c^2}} dt.$$

The time dilation formula is the same everywhere inside the shell.

You can understand why time is ticking slower inside the shell is that when you send a photon from inside the shell, it will be redshifted.

So although the spacetime is flat inside the shell, time still ticks slower, because it depends on the gravitational potential. An that is not zero inside the shell.

As was pointed out by @Arpad Szendrei gravitational time dilation depends on the gravitational potential. To answer the question we make use of Newton’s Shell Theorem according to which the mass $$M$$ of the shell can be thought as to be concentrated at its center for any point outside the shell.

Thus the potential outside is - $$GM/R$$, where $$R$$ is the distance to the center. Potential at any point inside - $$GM/r$$, with $$r$$ representing the radius of the shell. From this, it follows that for a distant observer time dilation is the same on the surface of the shell and everywhere inside it.