Long planet and Galileo thought experiment

[pervect]

Rather than attempt to go through this long thread, I'd like to suggest a better model of a "flat planet" - an accelerating spaceship. In particular, I mean the metric I describe
here.

It should be reasonably clear that the proper time of an object dropped from some height in this metric is constant, but that the coordinate time it takes to fall varies, just from considerations of symmetry.

 

[Jorrie]

Rather than attempt to go through this long thread, I'd like to suggest a better model of a "flat planet" - an accelerating spaceship. In particular, I mean the metric I describe
here.

It should be reasonably clear that the proper time of an object dropped from some height in this metric is constant, but that the coordinate time it takes to fall varies, just from considerations of symmetry.

Thanks for the link. I think the thread has concluded that Galileo was right for a 'flat planet' or uniformly accelerated lab, but there is a nagging question about what happens very near a supermassive black hole's horizon with a 0.8c horizontal velocity ball. Does it drop faster then a ball released from rest?

I've done some https://www.physicsforums.com/showpost.php?p=1689919&postcount=70" based on your earlier derivation of the radial and angular accelerations in a Schwarzschild orbit and came to the (perhaps erroneous) conclusion that the horizontally moving ball 'falls' faster in a local Cartesian frame.

-J