Why we won't notice anything special when crossing the horizon?

[jartsa]

More precisely, if the proper acceleration required to "hover" at the radius, above the horizon, at which the robot starts being winched, redshifted to infinity, were 1 g. (This also assumes that the robot is winched up slowly enough that its motion can be approximated by a series of static states at gradually increasing radius, and that the distance through which the robot is winched is small enough that there is no detectable change in the redshifted proper acceleration.) No object can be winched up from the horizon itself, and the surface gravity is the redshifted proper acceleration at the horizon. The redshifted proper acceleration at any point above the horizon will be less.

I still don't see what this has to do with the rest of the thread.

Why did I say the winching distance must be short? Oh yes, I thought the gravity field is quite inform but the gravitating energy increases rapidly, so the force increases.

I forgot that "unifom" gravity field is not uniform.

So when everyting is taken into account the force is quite constant, over quite large distance, like there was some kind of force field that is quite uniform. Right?

Earlier in this thread me and PAllen were arguing about this matter.

 

[PeterDonis]

So when everyting is taken into account the force is quite constant, over quite large distance, like there was some kind of force field that is quite uniform. Right?

The term "uniform gravity field" is somewhat problematic, as you have seen. Strictly speaking, the term does not apply in the presence of an actual gravitating body; it applies to the apparent "gravity field" seen by a family of accelerated observers in flat spacetime that all maintain a constant proper distance from each other. The term "Rindler observers" is often used to describe such a family of observers. However, as you note, the acceleration felt by such a family of observers is actually not uniform; the observers "lower down" feel more acceleration than the ones "higher up".

In the presence of an actual gravitating body, tidal gravity is present, which makes the field of an actual gravitating body vary with distance in a different way than the apparent "field" seen by Rindler observers in flat spacetime. (Also, the variation with distance depends on the mass of the body, whereas there is only one possible variation with distance for the acceleration felt by Rindler observers in flat spacetime.) I believe the term "uniform field" was used to describe the flat spacetime case to emphasize the fact that there is no tidal gravity in flat spacetime; but it can be confusing to realize that even in the absence of tidal gravity, the "gravity field" seen by Rindler observers still varies with position.

Since you have set your scenario in the presence of an actual gravitating body, the criterion for being able to treat the force felt by an object as constant is that tidal gravity is negligible over whatever distance you are considering. The larger the mass of the body, the larger the distance over which the force can be treated as uniform.