Throwing a string into a blackhole

[ice109]

if i threw a string from a great distance into a black hole what would happen? if something was attached to the other end of the string would that thing eventually get realed in?

 

[pervect]

The short answer is that either the string will break, or the object attached to the string will get reeled in.

There are physical limits as to how strong a string can be, one of them is imposed by the "weak energy condition", another limit is imposed by requiring that the speed of sound in the string can't be greater than the speed of light.

There is a rather detailed (and technical) analysis of this online at http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

which uses a relativistic elasticity model (called the hyperelastic model) to model the characteristics of the string.

The hyperelastic model is (relatively) easy to work with mathematically but will only give sensible results if the input parameters are restricted to a reasonable physical range.

The webpage includes some gif-movies of the simulation results, and also has some references to the literature on relativistic elasticity.

 

[ice109]

so i just skipped to the end cause i really don't know anything about GR and we have this

"Although a string lowered in this fashion appears doomed to break eventually, this example shows that there's no reason it can't survive intact not only after crit, but also after the bottom of the string has passed through the horizon according to the string's own definition of simultaneity. In other words, a spacelike slice orthogonal to the world lines of the string's elements can run all the way from the bottom of the string, on the far side of the Rindler horizon, to the point of unreeling, with the tension everywhere remaining well below the limit set by the weak energy condition."

so now suppose this string was wrapped around a generator. what then? if the string doesn't break and turns the generator we get power from the black hole? is there something I'm missing?

 

[pervect]

You should read a bit further:

Given some function of proper time which expresses the rate at which the string is being unreeled, there will be a time $\tau_{crit}$ after which no signal from the point of unreeling can reach the object at the end of the string before it passes through the horizon.

After $\tau_{crit}$, the only way to keep the string from eventually breaking (assuming it hasn't broken already) will be to continue to feed it out at an increasing rate. Clamping the string, attempting to pull the object back up, or even just feeding out the string at a constant rate, will all ultimately cause the string to break, though the exact time when that happens will depend on the physical properties of the string.

 

[Fredrik]

so now suppose this string was wrapped around a generator. what then? if the string doesn't break and turns the generator we get power from the black hole? is there something I'm missing?

1. You wouldn't be able to enjoy the benefits of this energy indefinitely, since the generator would get pulled closer to the black hole when you do this.

2. The process you describe doesn't move energy from inside the event horizon to outside, because the rope itself has lots of energy (E=mc² remember). So the process will put more energy into the black hole, not steal energy from it.

 

[pervect]

You can extract some of an objects rest mass energy by dropping it into a black hole, if that's the point of the original question. Black holes are often associated with very energetic "jets", for instance, and it is the gravitational energy of the infalling matter that helps power them.

http://www.space.com/scienceastronomy/blackhole_jets_040817.html

The black hole grows in mass by the 'energy at infinity' of the infalling matter, not by the rest mass of the infalling matter. This means that part of the energy (including the rest energy) of the infalling matter will go into increasing the mass of the black hole, and part will usually be radiated away during the fall in one form or other. So the total energy of the system stays constant, part of the mass of the infalling object is converted into various forms of energy and radiated away, the rest goes into increasing the mass of the black hole.

While energy conservation can be problematical in GR, a black hole isn't one of those cases where this issue arises. The black hole space-time is static AND asymptotically flat.

 

[Loren Booda]

From what I understand:

Let the string, marked off in equal lengths, to be attached to an observer. For the stationary observer well outside of the event horizon, the lengths will appear to Fitzgerald contract infinitely as the string leads toward this limiting surface. For the observer lowered through the event horizon on the string, the lengths conserve themselves locally, but in the direction of the apparent singularity one sees the event horizon as approaching a pointlike gravitational (and observational) collapse.