Re: How would length contraction do an object falling into a black hole?

Hi Stewart,

You asked what would be the combined effect of tidal stretching and relativistic length-contraction on an astronaut falling into a black hole.

That's an interesting question. It's probably easiest to think about it from the ill-fated astronaut's own perspective. In this perspective there is no length contraction - the length contraction is visible when someone in one freely-moving trajectory tries to make observations of someone in a different trajectory. One is always at rest with respect to oneself, so the astronaut does not see any contraction of him or herself.

However, near the black hole, gravitational forces are very strong and getting stronger very rapidly. The changes are so steep that, near the black hole (and within its event horizon) the forces on your feet are much stronger than the forces on your head. The forces eventually become strong enough to tear apart everything - spaceships, astronauts, feet, cells, even atoms - via ordinary mechanical forces. The astronaut will definitely notice him or herself being pulled to bits - fortunately this painful experience will last for mere microseconds. The bits will stretch out into a thin line as they fall towards the singularity. This all happens mostly outside of the event horizon; by the time anything crosses the horizon, it has been reduced to a string of nuclei and electrons (I think - no one really understands gravity at atomic length scales!). But nothing dramatic happens during the horizon-crossing itself.

Viewed from far away, you will indeed see the astronaut fall towards the hole and be "spaghettified" on the way. However, since the astronaut is moving away from you at high speed, you need to use relativity to determine what sort of distortions would occur. If the astronaut is falling away from you, there is a "Doppler redshift"; since light-information from the astronaut has to climb out of the gravitational field of the black hole, there is also a "gravitational redshift." These two effects (which in General Relativity would be lumped together) result in:

• light from the astronaut being reddened
• the astronaut's watch seeming to slow down, and
• (here's the answer to your question) the astronaut appearing shorter.

All of these visual effects apply when the astronaut is still outside of the event horizon - of course you cannot see anything inside, and moreover you' ll never actually see anything go in. And due to the time-slowing effect described in this link, it should be clear that eventually, viewed from outside, the astronaut will appear to be very short rather than very long.

Good question! And stay away from black holes!

-Ben Monreal