Large object entering a small BH

[PAllen]

Thank you guys.

So, it seems that even a 30 cm BH would cause the scientist (and the lab, and the Earth) to break up inside it. I don't understand, since we are told that a BH doesn't suck things up*. I thought a object only gets trapped inside a BH (and, thus, is destroyed) when it passes the event horizon. Is not it so?

* Therefore, I thought there would be no problem in having a 30 cm BH on a lab... (of course, apart from the other difficulties.)

It looks like several replies have clarified most of this, but I'll just add one more point. If the Earth were captured by a passing 30 cm BH (which is necessarily 30 times as massive as earth), at a distance comparable to several times the Earth moon distance, then the fact that one of the orbital partners is a BH would, indeed be irrelevant. You would just have a binary system stable for ordinary time scales (millions of years). However, the scenario I was responding to was an attempt to hit the Earth with the BH. In this case, while initially you might imagine the BH punching a hole in the earth, the rest of the mass would be captured in orbit, and then shredded to an accretion disk due to extreme tidal forces. A direct hit is hard to manage, but my point was that a near miss (e.g. hundreds of miles) would be equally catastrophic.

 

[pervect]

If you are more than 10x the Schwarzschild radius (for your 30cm radius black hole, that's 3 meters) you can apply Newton's formulae with only small errors. As previously mentioned, the mass of the BH would be about 30 Earth masses. At 3 meters, a Newtonian calculation gives you about 0.4 million billion times Earth's gravity (4*10 ^ 15 meters/sec^2 acceleration).

So a more reasonable question would be if you were at a location where the gravity of the BH was 1g so you could sit comfortably in your lab without being compressed into a flat puddle of goo, what happens if you lower an ultra-strong cable into the BH. Your lab would have to be about 6 Earth radii away for that, make it 24,000 miles or so. The answer to the revised question that is that if the cable has a finite tensile strength, it will break.

 

[Tio Barnabe]

So let me see if I got the point

A black hole doesn't suck up things by itself, but as it is a concentration of mass, it has gravity and, therefore, will atract other masses as any other body would do. Correct?

So, we can say that while on the outside of a black hole, (say) a scientist would be atracted to the BH as he would be by any other massive body, but once that scientist passes the event horizon, then GR predicts that he will not be able to go out anymore, this time not because of gravity, but because the space-time path inside the BH doesn't allow for this to happen. Correct?

 

[Ibix]

You are making a distinction between gravity and curvature that doesn't exist. Gravity is the curvature of spacetime (or, at least, so says GR). So a long distance from a black hole your path curves towards the hole because of spacetime curvature, and close to (or inside) the hole your path curves towards the singularity because of spacetime curvature. The definition of "inside the hole" is where the curvature is such that there are no outward-moving paths (not timelike ones anyway).

All pervect is saying is that more than ten Schwarzschild radii away from the black hole, Newtonian gravity is a good approximation and you can save yourself a lot of maths by using it. Nothing is different about the physics of gravity close to or far away from the black hole - it's all curvature. But the maths is horrible, and there's no significant loss of precision in using a simpler theory.

 

[jbriggs444]

So let me see if I got the point

A black hole doesn't suck up things by itself, but as it is a concentration of mass, it has gravity and, therefore, will atract other masses as any other body would do. Correct?

That is the Newtonian approximation. It is also what General Relativity predicts when masses are smallish and distances are largish. Newton models this "gravity" as a force. General Relativity models it as straight paths in curved space-time. Even outside the horizon.

So, we can say that while on the outside of a black hole, (say) a scientist would be atracted to the BH as he would be by any other massive body, but once that scientist passes the event horizon, then GR predicts that he will not be able to go out anymore, this time not because of gravity, but because the space-time path inside the BH doesn't allow for this to happen. Correct?

Once you are inside the event horizon, you are definitely in a regime where the Newtonian approximation is not at all accurate.