Question: Would you ever finish falling into a black hole?

Cesar Lopez-Monsalvo answered on 16 Jun 2011:

Hahaha! I loved the Captain Gravity title!

Scorpius

The answer to your question is yes, your fall will come to an end!!

There is a common misunderstanding between falling and watching someone else falling into a black hole. Black holes are interesting objects for many reasons. Lets make a “thought experiment” (my favourite kind since I am not a lab person). Imagine you and someone you don’t like very much agree to try the following. One of you will jump free fall into a black hole (no matter how) and while falling he/she will be sending a signal, say a flash of light, every second to the person that is watching. Now here is the “strange thing”:

1. To the person watching, the flashes will not seem to come every second. They will take longer and longer; first one second, then one minute, then one hour, then one day….then ten years, then a hundred years,…then a million years …and the last signal will never reach the departure point. Obviously the person watching will never see his/her friend actually crashing with the black hole. The point is that the number of flashings will not be very large….a hundred, say. But there will be a longer wait between two consecutive flashes each time. The last one will never actually be seen.

2. For the person falling, he/she will diligently send his flashes every second all the way to the black hole and in a hundred seconds, without noticing, that person would have crossed the horizon (the boundary separating inside and outside, see my answer http://ias.im/47.833). And in a 103 seconds he/she will cease to exist….not very nice.

[Note that I just made up all these numbers to illustrate a true fact, so don’t take the time scale very seriously] 😉

The difference between 1. and 2. has to do with the relation between space, time and gravity. If the two persons doing this experiment have a watch each, they can verify that both agree in the duration of a second. Once one of them starts falling, the “gravitational field” will change constantly his/her readings with respect to the one observing. That difference will grow as the falling person approaches the centre of the black hole.

As a side note, we don’t need a black hole to appreciate that effect. Something similar happens on earth. The clock inside the computer of a gps on the surface of the earth ticks at a different speed that the one inside the computer of a satellite in orbit. That is very important because if they cannot agree on the duration of a second, they would fail to tell you were you are with certain precision. Thus engineers have to take into account these gravity effects when designing these kind of devices.