Can a black hole be accelerated to go faster than the speed of light?

[solidon]

Can a black hole be accelerated to go faster than the speed of light?

I've heard that when dealing with the moments of inflation and also with relation to warp engines, space itself can move faster than light. I've also heard that a black hole is a region of space that can move.

So can it?

 

[pervect]

The very short answer is no, a black hole cannot be accelerated to go faster than the speed of light.

Of course, to say this we have to define how we measure the speed of a black hole at all. This process of defining is subject to some ambiguity. The definition I'm using is this:

The speed of a black hole relative to some observer (or the speed of some observer relative to a black hole) is the relative speed between the specified observer, and another observer who is stationary with respect to the black hole.

Using this definition of "speed", the speed of a black hole (or the speed of an observer relative to that of a black hole) is always less than 'c'.

 

[p4h]

I stumbled over this article:
http://archives.cnn.com/2002/TECH/space/10/03/black.holes/

Dunno how credible cnn is in terms of physics

But I thought it might have some relevance.

 

[George Jones]

I stumbled over this article:
http://archives.cnn.com/2002/TECH/space/10/03/black.holes/

Dunno how credible cnn is in terms of physics

But I thought it might have some relevance.

At a quick glance, it looks OK. Note the headline says "looks", and also this passage from the article:

"'Initially the jets have been launched at a velocity close to the speed of light. Due to an optical illusion, the jet pointed toward us appeared to move faster than the speed of light,' University of Paris astronomer Stephane Corbel said."

 

[p4h]

I didn't read all of it, I just saw the title and figured it might have a relevance in here. But I guess I should take time to read it next time :)

 

[George Jones]

It's a nice media article; it describes an interesting effect and a bit of a puzzle in a scientifically accurate way.

 

[solidon]

The very short answer is no, a black hole cannot be accelerated to go faster than the speed of light.

Of course, to say this we have to define how we measure the speed of a black hole at all. This process of defining is subject to some ambiguity. The definition I'm using is this:

The speed of a black hole relative to some observer (or the speed of some observer relative to a black hole) is the relative speed between the specified observer, and another observer who is stationary with respect to the black hole.

Using this definition of "speed", the speed of a black hole (or the speed of an observer relative to that of a black hole) is always less than 'c'.

Hmmm, but isn't the black hole a region of space? And space itself is believed by some to theoretically be able to go at faster than lightspeed(inflation, warp engines, etc). The mass is all in the singularity and the laws of physics don't apply there. So given that nothing with mass is involved(mass is in singularity) in the physics, why can't it go at c? And if it's simply a region of space(the singularity is not affected) why can't it go faster than c?

 

[daniel_i_l]

Hmmm, but isn't the black hole a region of space? And space itself is believed by some to theoretically be able to go at faster than lightspeed(inflation, warp engines, etc).

Actually, Einstein showed that gravity waves (you can picture them as waves of spacetime) move exactly at the speed of light. This is very fortunate because one of the reasons that he wanted a theory of gravity different than Newton's was because according to Newton's theory the gravitational effect is instantaneous and according to SR that's impossible.

 

[pervect]

Hmmm, but isn't the black hole a region of space?

Except for the singularity at the center.

And space itself is believed by some to theoretically be able to go at faster than lightspeed(inflation, warp engines, etc).

It depends on how you define speed. There are some hidden issues here with even defining speed in GR. So the fine print in my definition of speed was/is important.

For a reference on this, see for instance: Baez's GR tutorial

Preliminaries

Before stating Einstein's equation, we need a little preparation. We assume the reader is somewhat familiar with special relativity -- otherwise general relativity will be too hard. But there are some big differences between special and general relativity, which can cause immense confusion if neglected.

In special relativity, we cannot talk about absolute velocities, but only relative velocities. For example, we cannot sensibly ask if a particle is at rest, only whether it is at rest relative to another. The reason is that in this theory, velocities are described as vectors in 4-dimensional spacetime. Switching to a different inertial coordinate system can change which way these vectors point relative to our coordinate axes, but not whether two of them point the same way.

In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime -- that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime.
The mass is all in the singularity and the laws of physics don't apply there. So given that nothing with mass is involved(mass is in singularity) in the physics, why can't it go at c? And if it's simply a region of space(the singularity is not affected) why can't it go faster than c?

No two particles at the same point in space-time will ever have a relative velocity greater than 'c'. This comes from the fact that GR in a small enough neighborhood of a single point approaches SR.

It is possible to assign a meaning to the notion of a particle that is "stationary" with respect to the black hole, so it serves as a convenient way to define velocity. If we adopt this definition, then there is no way to exceed the speed of light relative to a black hole. This is because it is possible to have a particle that is stationary with respect to a black hole at any given point, and that it is not possible to have two particles with a relative velocity greater than 'c' at the same point.

In a similar sense, while the standard GR metric of the universe (a FRW metric) does not have all the nice mathematical features of the black hole metric, we can still single out a priveliged class of observers who move with the Hubble flow. And we can say that one's velocity with respect to the Hubble flow is always less than 'c'.

There is another definition of velocity used in cosmology that uses Hubble's law that exceeds 'c', but it is not the same definition of velocity as the one I used. Unfortunately, as the Baez quote shows, there are some conceptual difficulties in even defining exactly what relative velocity means unless two objects are compared at the same point in space. Note that greater than 'c' "velocities" with the defintion that gives them can only occur with distant objects, it is still true that no two objects at the same point in space ever have a relative velocity greater than 'c'.

 

[solidon]

Hmmm, this brings forth the question of warp engines and why they're still considered hypothetically plausible.

gravity can't move/warp space faster than light, a region of space(say a black hole) can't move faster than light, so what's the deal here? What is the difference when it comes to warp engines that allows them to still have some theoretical/hypothetical viability in the minds of many physicists?

If one somehow distorted a region of space around the black hole so that it/region resembled more a warp engine would it then be able to go at ftl(assuming it's possible to cause said spacetime distortion.)?

 

[yuiop]

Can a black hole be accelerated to go faster than the speed of light?

I've heard that when dealing with the moments of inflation and also with relation to warp engines, space itself can move faster than light. I've also heard that a black hole is a region of space that can move.

So can it?

Perhaps you read something like this wiki article? http://en.wikipedia.org/wiki/Ergosphere

"The ergosphere is ellipsoidal in shape and is situated so that at the poles of rotating black hole it touches the event horizon and stretches out to a distance that is equal to the radius of the event horizon. Within the ergosphere spacetime is dragged along in the direction of the rotation of the black hole at a speed greater than the speed of light in relation to the rest of the universe. This process is known as the Lense-Thirring effect or frame-dragging. Because of this dragging effect objects within the ergosphere are not stationary in respect to the rest of the universe, unless they travel faster than the speed of light, which is impossible based on the laws of physics."


From that point of view, objects stationary with respect to the spacetime within the ergosphere (or moving in the same direction) would be going at greater than the speed of light with respect to the rest of the universe.

I will leave it to the experts like Pervect and Chris to decide if that is a mainstream view or not

In a similar fashion, stars and galaxies billions of light years away can appear to be receding at greater than the speed of light away from ,due to the expansion of space, although they are always going at sub luminal speeds with respect to their own local space time.

 

[JesseM]

gravity can't move/warp space faster than light, a region of space(say a black hole) can't move faster than light, so what's the deal here? What is the difference when it comes to warp engines that allows them to still have some theoretical/hypothetical viability in the minds of many physicists?

Gravity cannot cause objects in the same local region of spacetime to have a relative velocity that's faster than light. But over nonlocal regions, depending on your choice of coordinate system things can indeed move apart faster than c (likewise, an object traveling through some region of curved spacetime can get from one location to another more quickly than a beam of light which does not travel through that region, although the light will still get there faster if it goes through the same region).