Understanding Tidal Forces on a Sphere: Do They Also Act Horizontally?

[exponent137]

In http://arxiv.org/pdf/gr-qc/0103044v5.pdf in page 6 it is written about a tidal forces on a sphere built up from test particles.
It is written that ball also starts to being squashed in the horizontal directions. I do not understand this. Because gradient of gravitational force is mainly in vertical direction. Is it also in horizontal direction?
What is mechanism for squashing in horizontal direction?

Is here at this ball of test particles any distinction to the tide on Earth caused by moon?

 

[A.T.]

Because gradient of gravitational force is mainly in vertical direction. Is it also in horizontal direction?

This is already true for Newtonian Gravity:

https://web.njit.edu/~gary/320/Lecture12.html

 

[exponent137]

Water in oceans is connected, Baez's test particles are not. Thus water must flow from elsewhere on vertical direction and it should flow elsewhere from horizontal direction. Earth gives backbone to water.
Is here any special difference to calculation because of these two reasons, or is this neglected?

 

[Nugatory]

Water in oceans is connected, Baez's test particles are not. Thus water must flow from elsewhere on vertical direction and it should flow elsewhere from horizontal direction. Earth gives backbone to water.
Is here any special difference to calculation because of these two reasons, or is this neglected?

There is no difference. We're calculating the changes in the magnitude and direction of the gravitational force at various points and those don't care whether they're acting on water or a cloud of test particles.

(As A.T. has already pointed out, this is not a relativity question - it's just classical gravity).

 

[wabbit]

There is a difference is how the oceans respond to those tidal forces, as a more or less incompressible fluid constrained in its motion as you noted, instead of free non-interacting particles - though as Nugatory said, not in the forces themselves.