Fishing in a Black Hole: Can It Be Done?

[magneticanomaly]

TL;DR Summary

If BH do exist, could a sufficiently small mass attached to a sufficiently strong string be lowered past the Schwarzchild radius, and pulled back out?

Summary:: If BH do exist, could a sufficiently small mass attached to a sufficiently strong string be lowered past the Schwarzschild radius, and pulled back out?

If BH do exist (see https://arxiv.org/abs/1406.1525), could a sufficiently small mass attached to a sufficiently strong, sufficiently long string be lowered (from a sufficiently powerful hovering rocket) past the Schwarzschild radius, and pulled back out? If not, why not?

 

[PAllen]

First, you should be aware that the paper you sight, while published in a reputable peer reviewed journal, is rejected by a large majority of researchers in this domain.

As to your question, no it would not be possible. Any path from inside to outside the horizon is spacelike, which means it more like a ruler than the path of a body. Paths going from outside to inside are timelike, thus normal paths of bodies.

[edit: reminding myself of this papers claims, which I last looked at over 5 years ago, I make a stronger claim. This paper is experimentally refuted by two major observations. It claims the would be BH have no horizon and a radius larger than the Schwarzschild radius. The latter claim is refuted by gravitational wave observations of BH mergers, and by the Event Horizon Telescope observations.].

 

[lomidrevo]

No signal can be sent from inside the event horizon to the rest of the universe. That applies also to electromagnetic forces holding your string together.

Edit: not mentioning any tidal effects which would probably break your string before it approaches the event horizon

 

[lomidrevo]

Btw. I cannot resist, what do you mean by

If BH do exist

They do exist! There is so much evidence that no scientists are questioning that.

 

[Orodruin]

Edit: not mentioning any tidal effects which would probably break your string before it approaches the event horizon

If the BH is sufficiently large, tidal forces near the horizon will be minimal.

 

[lomidrevo]

If the BH is sufficiently large, tidal forces near the horizon will be minimal.

Yes, right. The OP didn't specify the size/mass of the black hole, so when answering I had in my mind the most common case: stellar-mass black hole.

 

[jbriggs444]

Even if you could hoist the mass up to the event horizon (you can't) it would take infinite acceleration and infinite force to bring it up farther.

Locally, the horizon is an "outgoing null surface". This means that it is moving at the speed of light relative to any local inertial observer. If you are a finite distance ahead of it, you can maintain separation by accelerating away from it. The nearer you are to the horizon, the more acceleration is required. At the horizon, no finite acceleration will suffice.

Inside the horizon, any applied force (and its consequent acceleration) in any direction does not succeed in bringing the object upward. Instead it actually hastens the trip toward the singularity.

 

[Ibix]

Inside the horizon, any applied force (and its consequent acceleration) in any direction does not succeed in bringing the object upward. Instead it actually hastens the trip toward the singularity.

Although this is often stated, it turns out to be not quite true. If memory serves, maximum survival time comes from free-falling from rest an infinitesimal distance above the event horizon. If you don't start in that state, you can increase your survival time by accelerating to match trajectory with such an object.

I can track down the reference for that if you like.

 

[PAllen]

Edit: not mentioning any tidal effects which would probably break your string before it approaches the event horizon

Though not from tidal forces, this is still true in the sense implied by the OP. That is, if you imagine a hovering platform (it would have constant proper acceleration with some 'magic' thrust source to keep it there), lowering a body on a 'string' very slowly, then the force the string needs to apply to the lowered body approaches infinite as the body approaches the horizon (to keep the lowered body essentially hovering at each new position). The string would necessarily break for this reason.

You can have the string span the horizon under other scenarios, however, e.g. rapidly unspooling string that does not try to slow the body's fall beyond a fixed maximum force applied from string end to body.

 

[Dale]

@magneticanomaly
You might be interested in this page http://www.gregegan.net/SCIENCE/Rindler/RindlerHorizon.html

 

[PeroK]

If you don't start in that state, you can increase your survival time by accelerating to match trajectory with such an object.

I can track down the reference for that if you like.

I think I'd want it to be over as quickly as possible!

 

[PAllen]

Although this is often stated, it turns out to be not quite true. If memory serves, maximum survival time comes from free-falling from rest an infinitesimal distance above the event horizon. If you don't start in that state, you can increase your survival time by accelerating to match trajectory with such an object.

I can track down the reference for that if you like.

I used that formulation in the thread you refer to, but thinking more since then, I am not sure taking that limit leads to the correction once inside going to zero. The exact statement is more interesting:

Given any event inside the horizon, the proper time maximizing geodesic from that event to the singularity (which is a surface, not a point) is one that never extends back outside the horizon. That is why every infaller benefits by a course correction as soon as possible after horizon crossing. In the idealized Kruskal geometry, these geodesics are the family of free fall paths emerging from the white hole singularity and ending on the black hole singularity, that never go outside the horizon (there are others that leave and come back, but they are not part of this family). Together, they reach every interior event. In a more realistic collapse geometry, they intersect the path of infalling matter creating the BH inside the horizon, at some relative velocity to that infall path. Again, there is no way a later infaller will match such a path without an acceleration applied after horizon crossing.

 

[Ibix]

I think I'd want it to be over as quickly as possible!

I think you only have $15\mu s$ per solar mass of the black hole, even if you are a point particle and immune to tidal forces and radiation. So it's be over fairly quickly, whatever you do, for anything smaller than a super-massive black hole.

 

[PeroK]

I think you only have $15\mu s$ per solar mass of the black hole, even if you are a point particle and immune to tidal forces and radiation. So it's be over fairly quickly, whatever you do, for anything smaller than a super-massive black hole.

Glad to hear it.