This is our fifth and final installation of Physics of Rock Climbing (for now). Of course, I saved the most exciting stuff for last: BLACK HOLES! Feel free to skim over my general relativity (GR) piece from last time for some extra review of gravity.
We won’t be discussing Kerr black holes specifically, but nevertheless our hypothetical climber’s name today is Roy. Roy is a bit of an adrenaline junkie, and so he’s climbing right next to a black hole on a route called Robert’s Walk. The route extends away from the black hole in a straight line such that the start is nearest the black hole and the finish is farthest from the black hole. Our previous facts from GR still hold, of course. Roy experiences what Karl did, except much more noticeably since the black hole is magnitudes heavier and more dense than the earth. If you remember, we compared the earth to a bowling ball on a trampoline. A black hole on that trampoline would be something like the mass of a skyscraper in the volume of a grain of rice. You can imagine the difference our marble would feel on the trampoline if it had a bowling ball versus the really heavy grain of rice in the middle. If the trampoline were super tall. And super stretchy.
Having said that, there is something Roy experiences that Karl doesn’t. Roy can cross what’s called the Schwarzschild radius or event horizon. Earth’s Schwarzschild radius is smaller than Earth’s actual radius, so we can’t really see anything special there. However, since the black hole is so heavy and dense, the black hole’s Schwarzschild radius is WAY bigger than the radius of the hole itself. As you may have guessed already, the Schwarzschild radius is where everything goes black for Roy. He can’t see past it into the hole (hence the name black hole). Now let’s imagine the start of Robert’s Walk is a ledge, and the wall actually extends inside the Schwarzschild radius. Being a daredevil, Roy asks his belayer to lower him past Schwarzschild radius. Solemnly, his belayer complies, and he sees Roy approach, but never cross, the Schwarzschild radius. The closer he gets, the slower he appears to move. But this is only what his belayer sees. At the moment Roy is at the Schwarzschild radius, any light he emits back is frozen in time forever, and no one inside or outside of the hole will ever see it. Once he crosses the Schwarzschild radius…well, we don’t really know. We do know, however, no matter how hard he climbs, he will never be at rest, let alone ever climb back up to his belayer.
One interpretation is that space and time somehow switch meanings. In other words, Roy could experience space as we experience time (a flow where we can never see forward) and experience time as we experience space (we can’t really imagine what this would be like). Another possibility is that Roy emerges from the other end of the hole at a white hole. This white hole could be on the other side of spacetime (he would have traveled through a wormhole!). One thing we do know is that if Roy actually tried to do this, he would be dead long before he reaches the Schwarzschild radius. The force at his feet would be much greater than the force at his head, and he would snap/get squished. It would be like hanging a couple tons on Roy’s feet while he is hanging from a pull-up bar. Yikes.
The moral of the story is do not try this at home or at your nearest black hole.
Thank you for exploring the interface of physics and rock climbing with me! It has been an absolute pleasure, and if there’s anything else I can expand on, please let us know!