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This question already has an answer here:

First of all, this is a thought experiment regarding faster-than-light communication.

Say you had an immense hollow planet that was made of some heavy material such as neutron-star dust.

Due to the mass of the planet, the speed of light on the surface is slowed down by several percent due to gravitational time dilation.

But the planet is hollow. Since the gravitational force inside the planet is zero, the speed of light in the interior will be faster than that on the surface.

If we were to run a fiber-optic cable from the surface through the interior, would we be able to communicate faster than the speed of light, as far as the denizens on the surface were concerned?

If yes, would this cause a paradox of any sort?

References:

Gravitational time dilation: https://en.wikipedia.org/wiki/Gravitational_time_dilation

Shapiro delay: https://en.wikipedia.org/wiki/Shapiro_delay

StackExchange: Is spacetime flat inside a spherical shell?

StackExchange: Does gravity slow the speed that light travels?

UPDATE:

This question seems to be answered here: Time Dilation inside a hollow shell

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marked as duplicate by Kyle Kanos, Community Feb 24 '17 at 16:07

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Two points. 1 frame of reference considerations and 2. Can we not do this already bearing in mind the speed of light in water versus vacuum, say, is 75 percent. What's happens there with a half filled with water fibre optic cable.? $\endgroup$ – user146020 Feb 23 '17 at 21:12
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    $\begingroup$ Possible duplicate of Time Dilation inside a hollow shell $\endgroup$ – Yashas Feb 24 '17 at 6:50
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Its not that the speed of light changed, it's the speed of time. This article may help. https://www.sciencenews.org/article/center-earth-younger-outer-surface

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  • $\begingroup$ Would the question still be applicable, if the speed of time differed between the interior and surface of the hollow planet? The "fast time" section would be able to communicate faster than the "slow time" section by sending signals through the surface. $\endgroup$ – Derek Ross Feb 23 '17 at 21:36
  • $\begingroup$ No, they still communicate at light speed, measured everywhere locally. Time can change, speed of light can't $\endgroup$ – Bob Bee Feb 24 '17 at 1:45

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