These Level 2 videos analyze General Relativity topics that are a bit contentious.
In this video, we ask, “With the speed of light going to zero at the event horizon, can you actually cross it?” The standard answer is often formulated imperfectly. As an analogy we describe an artificial intelligence (AI) on a pendulum, with a clock rate that varies depending on angular speed.
Let me elaborate a bit.
There is a very common confusion, among us physicists, that conflates the proper time T of an infaller (finite time), with the Schwarzschild time t to reach the event horizon (infinite time). The latter, t, is not “just a coordinate” but physically measurable as the Shapiro delay (one of four classic tests of GR).
Thought experiment: shoot two photons, A and B, toward a black hole. Plot this in Schwarzschild coordinates, (r, t). Photon A bounces off a mirror a distance epsilon outside the event horizon, and returns after t = 1 billion years. (This is the Shapiro delay.) Photon B continues toward the horizon. But can we say that it did cross? There could be another mirror at 0.001*epsilon, so that B bounces and returns after 1 trillion years. Given the possibility of a bounce, you cannot say that B “has crossed” the event horizon.
For a non-evaporating black hole, we can map infinite-t to finite T: no problem, see for example Kruskal-Szekeres coordinates. For a finite-t, evaporating black hole you cannot do this.