# How does time behave inside a massive spherical shell?

According to General relativity the clocks in our satellites in the atmosphere tick faster than those on Earth, as they are farther from the gravitational well of Earth and are free falling.

According to Newtonian mechanics and Gauss theorem, a hollow massive spherical shell has no net gravitational field at any point inside the shell as the geometry cancels out the pull from each extrema.

I would imagine that this does not change in GR (am I wrong?), an object inside should be free falling. But does time behave different inside the shell and outside very far from the shell?

• Possible duplicate: physics.stackexchange.com/q/43626/2451 – Qmechanic Nov 27 '17 at 13:39
• FWIW, gravitational time dilation is a function of the gravitational potential, not the field strength. – PM 2Ring Dec 30 '19 at 12:11

Now imagine two persons, one inside, the other outside. The 'inside' one sends radio waves at some frequency. Let's say the frequency of radio waves he transmits is $N$, the transmission time is $t$ so that the transmission has $N*t$ full periods.
His colleague will receive a transmission having $N*t$ full periods as well.