I’d think of it in terms where you are “falling” into the black hole, you are not at a standstill (even on a surface like the floor you are standing on, we are still “falling” towards the center of the earth.Â Its just that the surface provides an equal force in the opposite direction which counteracts this fall).
Yes, it’s being in a gravity well. And I realize that you “fall” into a black hole as well and that the gravity well in a black hole is too steep for light to escape from.
Therefore, you must first attain a speed greater than the rate at which you are “falling” before you can make any progress towards the event horizonÂ
This is what I have a problem with. Certainly the speed of “descent” into Earth’s gravity well is greater than 1 m.p.h., yet I can get out of the gravity well by going 1 m.p.h if I do it long enough (straight up, for 300 hours).
Another way to look at it is in terms of the energy required and convert this energy to velocity.Â By the time you climb out of earths gravity well at 10 mph, you have used the same amount of energy as if you had started at escape velocity.
This seems right. Lets assume the energy of accelerating to 17,000 mph is the same as the energy required to go 10 mph for 50 or so hours.
In the case of a black hole, you would need the equivalent energy as if you started faster than the speed of light (which you won’t have)
So it goes back to infinite energy. But there’s not infinite gravity! Let’s say we’re in the gravity well of an object that requires an escape velocity of C-1 (speed of light -1). Given enough time and energy, we can escape the gravity well going at a very slow speed. And it woudn’t require anything close to infinite energy (or would it? I wouldn’t think so…). However, you are saying that once escape veolicty reaches C, there is no going back out. It doesn’t seem logical that a one mile per second difference is going to require an infinite amount of energy.