[Space] A question about Black Holes

[Bioman222]

So, from what I've heard, black holes are so massive, even light can not escape. Now, I haven't gone through much education on physics, but here's my question.

If black holes are so massive that light cannot escape them, doesn't that make their gravitational speed greater than the speed of light? Doesn't that break special relativity? What am I missing here?

[Ravenchant]

Gravitational "waves" do propagate at the speed of light, but AFAIK this isn't breaking anything. To be in orbit around a black hole, your centripetal force simply has to counter the gravitational acceleration. Inside of the event horizon, the required speed exceeds c. Since nothing can travel faster than c, well...stuff can't get back out.

[jfull]

I don't think there's any such thing as "gravitational speed"

[Accelerando]

I don't think there's any such thing as "gravitational speed"

I don't think there's such a thing as productive discussion consisting solely of syntactical nitpicking

Indeed OP, the escape velocity becomes greater than the speed of light at the event horizon. Roughly speaking. It's not certain what happens beyond that point, but it doesn't break relativity to have an escape velocity greater than light, so long as you aren't directly accelerating to FTL speed.

[Woopert]

Good question, I enjoyed reading these posts and the thread!

[Vanamonde]

Do you know what "escape velocity" is? To make an example, let's say you fire a canon ball straight up. It will be moving quickly at first, but earth's gravity will pull it down and slow it until it falls to the ground again. If the cannonball goes faster, it will get higher, but will still fall. But there is a speed, which can be calculated, at which the cannonball will move ever more slowly, but its outward speed will never be reduced all the way to zero. It will keep moving away from earth forever, and escape earth. That calculated speed is the escape velocity. Obviously, the more massive something is the stronger its gravity will be, and the higher its escape velocity will be.

A black hole is a mass whose escape velocity is higher than the speed of light, and since nothing we know of can go faster than light, this means nothing can escape from within a black hole*. So extremely massive objects can have an escape velocity higher than the speed of light, but since distance from the center is also a factor, an extraordinarily compressed mass can also be a black whole, even if it is (to use the usual example) only as massive as a medium-sized hill, with a physical size of a pea or smaller. So it's not so much the mass of the thing that makes a black hole, but whether there's a distance from the center at which the escape velocity is higher than the speed of light.

Relativity explains why nothing can go faster than light, so black holes exist not in defiance of relativity, but because of it.

*I'm leaving out Hawking evaporation because a) I don't really understand it, and I'm trying to write a brief and clear explanation.

[WestAir]

What the OP is asking is:

If gravitons exist, and gravitons propagate at C, wouldn't a graviton need to travel faster than C to deliver the information of the singularity to the outside universe? If gravity propagates at C, and the curvature of space-time is bent in such a way that gravity must propagate faster than C to reach objects away from the singularity, how does that not violate causality?

It's certainly an enticing query. Everything I've read on singularities suggest that within the event horizon, space-time is bent in such a way that all vectors lead towards the singularity. How then does gravity find a vector back to normal space?

The answer could simply be that gravity isn't affected by spacetime, that gravity isn't affected by its own force, or that gravity isn't transmitting any information at all. I've always wondered if this meant gravity could be used for FTL communication. Photons stand still at the event horizon - gravity does not.

[K^2]

Well, gravitons are tricky to talk about. There is not really a perfectly self-consistent description of them. But we can talk about photons. We've said that light can't get out, but black holes can have an electric charge. And then they do produce an electric field. If you've heard of gravitons, you probably know that photons carry electric field. So the million dollar question is, if photons can't get out of the black hole, how come it can still have an electric field.

And the reason comes from differences between virtual particles and real particles. The word "real" is just used to distinguish them from virtual particles. Kind of like "real numbers". It doesn't make the other ones fake, or anything. The other term for them is "mass shell particles," but that requires understanding of what a mass shell is. In simplest terms, it means they have a relationship between their mass and momentum. They have a number of properties, but most importantly, they propagate through space the way you expect a particle to propagate. They move in direction of their momentum, and if they have mass, the velocity relates to the momentum. If they don't have mass, like the photons, then they propagate at the speed of light, but still in direction pointed to by their momentum.

Another important bit is that they follow normal Relativity rules. All real particles travel along time-like trajectories. If no forces other than gravity act on them, they move along space-time's geodesics, which are the closest thing to a "straight line" in curved space-time. Inside the black hole, all time-like trajectories lead into the center of the black hole. That's why nothing can escape. In order to go from a time-like trajectory to a space-like trajectory, one must travel faster than light, and real particles simply cannot do that.

Virtual particles play by different rules. For a virtual particle, relationship between the way it propagates and its momentum is nowhere near as rigid. It can carry momentum pointing one way to a target located in completely opposite direction. It does not, necessarily, have a well-defined mass. Though, it can still be massless. Most importantly, it can follow time-like paths. There are other limitations, however. They can only be force-carriers. They cannot simply fly off into the distance. They have to go from source of the force they carry to their target. They can take really odd paths getting there, but they can't go anywhere else. And they do have limited range. For massless gauge bosons, such as photons, the range limitation gives you inverse square law. For the massive ones, like the Z and W bosons of weak interaction, the range is far, far shorter. Which is part of why weak interactions are, well, weak.

Because virtual particles can take detours, they aren't bound to time-like geodesics like the real particles are. And they can find their way out of the black hole. But as noted before, the only thing they can carry is the interaction force between the black hole and whatever happens to fly by. Since they can't interact with anything along their path, they do not violate cosmic sensor.

So this is why electric field can escape the black hole, while light does not, despite both being carried by photons. Gravity is going to work in a similar way. Black hole does induce gravitational field in its vicinity, but no gravitational waves can escape it any more than light can. Any self-consistent description of gravitons as a particle would have to have a similar distinction between real gravitons and virtual gravitons to account for this.

One last note. If you are wondering if this is all related to Hawking Radiation, yes, it is. Both are effects from Quantum Mechanics based around the fact that particles don't have to stick strictly to time-like trajectories. But Hawking Radiation does have quite a few other things going on.