We Will Never See Anything Falling Into a Black Hole Unless We Fall In Too!

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If we were to look towards a black hole and watch someone falling towards it, we would see them getting closer and closer to the event horizon, and rather surprisingly we would see them slowing down more and more... but we would never ever see them falling in. Let’s look at a simple diagram that helps us understand exactly why this happens.

We start by plotting out a simple position-time graph, showing how objects move through empty spacetime. A useful example is how a photon moves. But because this line would be really shallow on our graph, we can rescale the axes by multiplying the time axis by the speed of light, c. This way, our photon is represented by a nice 45 degree line on the graph. We can then choose units so that c = 1.

This same diagram can be used to represent the inside and outside of a black hole. One side of the 45 degree line represents the outside, the other the inside. This isn't intuitive, so here is a useful Wiki page to help: en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates

We then assume that two of our friends, Alice and Bob, are near the black hole. From her perspective, Alice stays a constant distance away from the black hole at all times. However Bob, from his perspective, falls in.

Using just simple 45 degree lines to show the fastest form of communication that Alice and Bob can have, we see how Bob can not send any signal to anyone outside the black hole once he's inside. We also see how Alice sees Bob slowing down as he approaches the event horizon. In fact, she will never see him falling into the black hole. Instead she will see his movements go into slow motion, and even his heartbeat slow infinitely. All of this despite Bob having clearly passed through the horizon from his own perspective.

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Chapters:
0:00 - We will NEVER see anything fall into a black hole!
0:54 - A simple diagram with huge insights into relativity
2:53 - Wait - the same diagram represents a BLACK HOLE?!
4:31 - A case study with Alice and Bob
6:21 - Remember, we got all of this from a simple graph