Whats the deal with black holes and "no information from inside the event horizon can leave"?

Question

I don't know if this would fall under the other questions but I have always been confused by this... Information has left the black hole; its mass, rotation, location, and a few other properties. My problem has been that a true singularity should collapse the space around it and become separate from the universe as being able to observe the effects of a singularity breaks the fact that it is a singularity.

If I see a black hole I can already tell its mass and be effected by the gravity of an object which I can receive no other information from. This would break things too!

Let's just say I am an all powerful being who can do almost impossible things, but I still have to follow the laws of the universe. I decide to create a gravity observation station in orbit which uses lasers to see very small changes in the black hole. It also has a teleporter of sorts.

I then enter the black hole and construct another station, this one however uses small black holes and impossibly powerful thrusters and materials to do certain things. Its purpose is to manipulate and sustain a small black hole "orbiting" the inside of the bigger black hole (being sustained, barely, by the station) it then changes the direction this smaller black hole orbits in a kind of binary way.

I then step into a "teleporter" converted to binary instructions and encoded into these gravitational and rotational information. (Let's just say the station has no lifespan) and this station over a huge amount of time begins to piece together this code, and reconstructs me in the "teleporter" on board.

Have I just circumvented the event horizon using disclosed information available to me? Why would or wouldn't this work because for what I see being able to describe a black hole violates the properties of the black hole.

Answer 1

You are right in that, if you could send a message of any kind from inside a black hole then there is no magic required rebuild you from the information about you. If you could send even a single bit of information, then the black hole wouldn't be so black. You want to do this using the rotation of the black hole.

This doesn't work, for various reasons.

Information has left the black hole; its mass, rotation, location, and a few other properties

The mass etc is a property of the black hole, not information travelling from inside the black hole. The reason is that you can't manipulate them in the way you describe, so they can't be used to send a message.

I then enter the black hole and construct another station

Here is your first problem. From the frame of reference outside the black hole, there is infinite time dilation at the event horizon. Hence you never quite reach the event horizon, nor enter the black hole.

From the frame of reference of the infalling person, the event horizon is crossed. So let's somehow pretend that you are now inside the event horizon.

Its purpose is to manipulate and sustain a small black hole "orbiting" the inside of the bigger black hole.

You can't orbit, you can only fall. The orbital speed is higher than the speed of light, so you will reach the singularity, as surely as you will reach next Tuesday. Your time has now been infinitely dilated, so events that take happen in finite time for you, take an infinite amount of time in the frame of the outside observer, so that makes sending a message using variation in rotation impossible.

Finally, from inside the black hole you can't change the total mass or rotation. The angular momentum of a closed system is conserved, so if you use your thrusters to change the direction of the small black hole you are carrying, the total angular momentum of the black hole remains constant. You can't change the total angular momentum with thrusters if you include both the angular momentum of the ship and the angular momentum of the gas ejected by the thrusters.

Similarly you can't change the total mass or location of the black hole from inside the black hole. And you can't do anything in a finite time from the perspective of an outside observer.

Thus no information can be encoded in the observed properties of the black hole.

Answer 2

Gravity curving spacetime causes the direction of time (along with the local speed of light) to tilt inwards. A black hole occurs when the time axis tilts so far that the entire future points into the black hole. Thus, you can't escape from a black hole for the same reason you can't escape from the future into the past. That would require time travel. And you can't get information from inside a black hole for the same reason you can't receive messages from the future.

The stuff you can see from the outside is actually looking back at the past, from the formation of the black hole up to now. You can only see and be affected by things in your past - all the events that can send light signals to you. Sitting outside the black hole and tracing your past back, the spacetime curvature means you find your past gets tilted away from the black hole so it never enters the event horizon. You can see the effect of all the stuff as it falls into the black hole, right back to its beginning, but you can't see it past the horizon because that's not inside your past, and never will be. The information about the collapse has been hovering just outside the horizon, inching outwards at the local speed of light for millions of years, until it finally escapes just as you get there. You don't get that information about the mass and angular momentum from inside the black hole, you get it from the history trapped just outside the horizon and slowly leaking out.

If you drop inside a black hole and fire thruster rockets, the combined mass, momentum, angular momuntum etc. of you and the rocket exhaust remains the same. Rockets only seem to move things because we commonly ignore the exhaust. You head one way, the exhaust heads the other, and the centre of mass of the combined system of you-plus-exhaust stays exactly where it was. And the exhaust can't escape the black hole either. Thus, it doesn't matter what thrusters you fire, you can't change the total momentum or angular momentum that is inside the black hole once you're inside.