Laying a rope into a black hole very fast

[jartsa]

So, I lay a rope into a black hole, rope leaves the reel at velocity 0.99 c.

When I observe the lower end of the rope, I never see it reaching the event horizon.

Can I see some slack rope somewhere sometime?

 

[Dale]

See the section entitled "String Unreeled at a Constant Rate"

http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

 

[pervect]

It might be useful to consider what an observer colocated with you at t=0 and moving with the rope would see.

Said observer would fall into the black hole at some finite proper time $\tau$ on his wristwatch. He'd see the event horizion as a lightlike surface approaching him at "c". Assuming a large black hole and ignoring tidal effects, the distance to the event horizion from the ropes frame of referece would be $c \, \tau$.

Meanwhile the ship would be flying away from the black hole and accelerating, laying out more rope. When the front of the rope reaches the event horizon, the ship would have p.ayed out approximately $.99 \, c \, \tau$ meters of rope ignoring the acceleration of the ship. Taking into account the acceleration of the ship the rope must stretch, as Egan has indicated.

Trying to consider things in the Schwarzschild frame isn't going to really work well, as our intuition of what a rope "should do" works best in a frame that's co-moving with the rope.

 

[.Scott]

So, I lay a rope into a black hole, rope leaves the reel at velocity 0.99 c.

When I observe the lower end of the rope, I never see it reaching the event horizon.

Can I see some slack rope somewhere sometime?

Obviously, at the moment the tail end of the rope leaves the reel, it will be slack and observable. Tidal effects would tend to cause the center of the rope to be taut, but the observed "scrunching up" of the rope as you observe it approach the event horizon would not be the result of slackness.

 

[jartsa]

See the section entitled "String Unreeled at a Constant Rate"

http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

So this unreeling does not work as I planned. The rope has to break, if the unreeling rate is constant. Ok, thank you.

 

[jartsa]

Obviously, at the moment the tail end of the rope leaves the reel, it will be slack and observable. Tidal effects would tend to cause the center of the rope to be taut, but the observed "scrunching up" of the rope as you observe it approach the event horizon would not be the result of slackness.

How can rope be scrunched up but not slack??

 

[jartsa]

It might be useful to consider what an observer colocated with you at t=0 and moving with the rope would see.

Said observer would fall into the black hole at some finite proper time $\tau$ on his wristwatch. He'd see the event horizion as a lightlike surface approaching him at "c". Assuming a large black hole and ignoring tidal effects, the distance to the event horizion from the ropes frame of referece would be $c \, \tau$.

Meanwhile the ship would be flying away from the black hole and accelerating, laying out more rope. When the front of the rope reaches the event horizon, the ship would have p.ayed out approximately $.99 \, c \, \tau$ meters of rope ignoring the acceleration of the ship. Taking into account the acceleration of the ship the rope must stretch, as Egan has indicated.

Trying to consider things in the Schwarzschild frame isn't going to really work well, as our intuition of what a rope "should do" works best in a frame that's co-moving with the rope.

$.99 \, c \, \tau$

I suspect frame jumping there. To obtain a distance, a velocity measured somewhere is multiplied by a time measured elsewhere.

EDIT: I see, the velocity was some rope segment's idea about the velocity of the ship. So no frame jumping.

 

[Nick O]

How can rope be scrunched up but not slack??

Not knowing the math of black holes, my naïve answer would be "compression". The observed density of the rope would increase.

I could be wrong, but if I am wrong I'm sure I will be corrected.

 

[Dale]

The rope has to break, if the unreeling rate is constant.

Yes, it must break.

 

[.Scott]

How can rope be scrunched up but not slack??

In the same way that a rope traveling at near the speed of light will appear flattened, even if remains taut.