The measurable position of a black hole's event horizon

[Cheap Astronomy]

I'm imagining a static context where you have a large black hole that doesn't change in size or mass and isn't rotating (i.e. a hypothetical situation). It has an event horizon which, from a certain distance, you are able to measure an exact location for. My question is, if you moved much closer to that exact location (and hence began to descend much deeper into the black hole's gravity well) would the location of that event horizon measurably change (with respect to you, the observer)?

I guess part of this question is whether, as an observer, an event horizon is always going to be a bit further beyond where you are - i.e. you can never know that you have 'crossed' an event horizon, with respect to what an distant observer may surmise.

Thanks!

[grant hutchison]

Setting aside the difficulty of measuring an exact position for the event horizon ...
The event horizon is a global property of spacetime, separating those spacetime locations that can emit photons with trajectories that end at infinity from those location whose photons have trajectories that end at the singularity. Since that property is the same for every observer, then the position of the event horizon is the same for every observer.

Grant Hutchison

[Noclevername]

I guess part of this question is whether, as an observer, an event horizon is always going to be a bit further beyond where you are - i.e. you can never know that you have 'crossed' an event horizon, with respect to what an distant observer may surmise.

If you get to the point where you detect photons emanating from the inside of the BH, you've obviously crossed the point where light cannot escape.

In a stellar-mass BH any observer would have been spaghettified, torn apart by concentrated tidal stress, before reaching the horizon; but a huge supermassive BH could conceivably have a weak enough tidal force to allow for intact entry.

[grant hutchison]

If you get to the point where you detect photons emanating from the inside of the BH, you've obviously crossed the point where light cannot escape.

It would be difficult to detect that point, however, without foreknowledge of the location of the event horizon.
Inside the event horizon, you'd actually be catching up with photons which had been emitted outwards, but were moving inwards--just winding down the radial coordinate more slowly than an infalling observer. So as you crossed the horizon feet-first, while observing your feet, you'd see no particular change as you moved from outside to inside. Setting aside the gravitational effects (and basic biology) for a moment, there would be a last photon reflected by your feet, shortly before they hit the singularity, which your head could catch up with and observe at the moment it encountered the singularity--so there would be a short period in the lifetime of your feet that would be unobservable by your head, because all the photons from your feet during that time period would reach the singularity before your head. In other words, infalling observers acquire an apparent horizon which is observer-dependent--there are spacetime events from which they will never receive photons. This is distinct from the invariant absolute horizon of the black hole, however.

Grant Hutchison