[PmbPhy]

From the original post: "Trying to get this relativity thing..."

Ahhh! I understand now. For some reason I thought you only had special relativity (SR) in mind because people almost always study SR before they study general relativity (GR). Thanks for making that clear.

[evan_au]

can gravity force an object to reach light speed at the event horizon of a black hole?

For a "distant observer", an object can reach just over c/3 before it disappears inside the event horizon.

If you scroll down to the graphs and equations on the following web page, you will see that the answer is "yes and no", all depending on your frame of reference.
http://physics.stackexchange.com/questions/170502/will-an-object-always-fall-at-an-infinite-speed-in-a-black-hole

[jeffreyH]

can gravity force an object to reach light speed at the event horizon of a black hole?

For a "distant observer", an object can reach just over c/3 before it disappears inside the event horizon.

If you scroll down to the graphs and equations on the following web page, you will see that the answer is "yes and no", all depending on your frame of reference.
http://physics.stackexchange.com/questions/170502/will-an-object-always-fall-at-an-infinite-speed-in-a-black-hole

Quite a while back now I did produce a set of graphs much like those of John Rennie in the linked thread. I was never convinced by some of my own conclusions. I may revisit this with a new perspective.

[Arthur Geddes (OP)]

"Apparent horizon" compelled me to look up "Photon sphere:" https://en.wikipedia.org/wiki/Photon_sphere & i wonder if these are essentially the same thing to a falling observer...?

Note "ds=o (a light-like interval)", i.e. relative to the photon.