relativistic effects on planetary shear [tidal forces]

nearc

before i ask my question i want to review two points:

1. place a body like a moon or a planet near a black hole, as the body approaches the extreme gravity affects the body deferentially.

2. review the tidal forces on Jupiter's moon Io leading to volcanic/tectonic consequences.

now take an identical copy of the earth and let it head through space with a velocity close the speed of light. even at these fantastic speeds nothing would be different on this new earth as compared to the original. however, the copy earth is still rotating so the side that is rotating into the direction of travel is getting even closer the speed of light. while the opposite side rotating away is going slower. even though this difference in velocities is only about 1 km/s can speeds sufficiently close to the speed of light yield a differential tidal force across the planet resulting affects on the geologic behavior of the planet [i.e. earthquacks, tectonics, etc...]?

PatrickPowers

As far as the copy earth is concerned it isn't moving at all, so there would be no stress. In fact since there is no moon, there would be less stress.

You COULD include the moon. Nothing would change. Physics is (are?) the same in every inertial reference frame. It might look strange to an outsider, but that's just too bad. Our Earth would look that way to an observer moving by at relativistic speeds.

nearc

yes that is the standard answer [i.e. the internal frame of reference can be treated as if it were a rest] and in most cases that is true, but in some of the extreme cases not necessarily; i want to look closer at these extremes. if our copy earth was headed into a black hole to an outside observer their would be a time dilation but observers on the planet would not think time was slowing down: yet, bad things will happen to this planet.

so lets pull our copy earth out of the black hole and place it back on its near speed of light velocity and since it is rotating then one side of the planet will be much more massive than the the other, would this not lead to tidal forces? [these are like the black hole tidal forces not moon-ocean tides]. plus the rotating will constantly change the parts the planet that are heavy and light.

Drakkith

There is no stress. Contrary to popular belief, moving at high velocities does not increase your mass. Objects moving near the speed of light do not collapse into black holes. It is only when you compare two different frames that you can even include things like kinetic energy into it. In such a case the energy would be found within the entire Earth, not just one side of it. Only then can you look at the different sides of the Earth and how it is rotating.