Event Horizon of Telescope Through Earth: Does It Exist?

[Tantal]

Assume we drill a hole through the Earth - through the center towards the other side. Then we use a telescope, point it through the hole and observe stars on the other side of the earth. The telescope experiences a constant acceleration from Earth's gravitation. Accelerated movements have an event horizon. Is the sight of our telescope limited by this horizon?

Answer #1: Yes. The telescope experiences a constant acceleration of 1g, so any star beyond the distance d=c^2/9.81 (~ one light year) is not visible. Furthermore, Einstein's equivalence principle (the comparison with an accelerated rocket) favors this answer.

Answer #2: No. The position of the telescope relatively to the stars does not change. It is the same as for any other position on Earth's surface, so Earth's gravitational accelaration does not matter. Furthermore, there would be no problem for another telescope on the far end of the hole in observing faraway stars. The photons of such stars which made it up to the far end telescope should have no troubles to pass the rest of their journey through the hole - like photons of a flash light positioned at the far end of the hole.

Because of the flash light argument Answer #2 seems to be the only choice. But then Einstein's equivalence would not hold. Where is the flaw in these answers?

 

[PeterDonis]

Because of the flash light argument Answer #2 seems to be the only choice.

Yes, answer #2 is correct. Answer #1 would be correct if spacetime were flat, but it isn't.

But then Einstein's equivalence would not hold.

The observations you are talking about are not local; they are not confined to a small enough region of spacetime that tidal gravity is negligible. So the EP does not apply, and the observations you describe do not mean the EP does not hold.