B Formation of a black hole using acceleration

[Isaac Hart]

TL;DR Summary

Interesting way/circumstance in which a black hole might form.

Here is my question

Imagine if you had an object, this object is then accelerated. The process of acceleration bends space-time. For a black hole to form there must be extreme curvature of spacetime. Therefore, accelerating an object at such a high rate could create a black hole.

I am not referring to the mass of the object; however, I presume that the greater the mass of the object the less speed it would have to be accelerated in order to make a black hole.

Please correct me if I am wrong, I would very much like to know more about black holes. It is a very interesting experience.

 

[Ibix]

The process of acceleration bends space-time.

This is incorrect, so no, you cannot become a black hole by moving fast. The easy way to see this is this: you are currently moving at 99.9999% of the speed of light as measured by a cosmic ray particle. Do you feel like a black hole?

 

[Isaac Hart]

This is incorrect, so no, you cannot become a black hole by moving fast. The easy way to see this is this: you are currently moving at 99.9999% of the speed of light as measured by a cosmic ray particle. Do you feel like a black hole?

Please provide more detail, I am talking about acceleration not constant speed. Acceleration bends space-time speed does not. You don't need a particle/object to move really fast - all you need is it to accelerate.

Thanks for the feedback though.

 

[PeterDonis]

Acceleration bends space-time

No, it doesn't. Acceleration is bending of a worldline. It is not bending of spacetime and does not cause bending of spacetime.

 

[Isaac Hart]

That's interesting, I will have to find out what a worldline is. Alternative point: Due to the 'equivalence principle' which is that to accelerating observers it appears as if spacetime is bent. Does that mean that if a particle was accelerated at such a high rate would experience the event horizon of a black hole? If not then how is that so please.

 

[ergospherical]

Imagine if you had an object, this object is then accelerated. The process of acceleration bends space-time. For a black hole to form there must be extreme curvature of spacetime. Therefore, accelerating an object at such a high rate could create a black hole.

That's not quite true, but interestingly, it's not a crazy comparison either. The geometry near the event horizon of a Schwarzschild black hole, for example, is isometric to Rindler spacetime (explicitly, make the coordinate transformation $r = 2M + x^2/(8M)$ for small $x$), which describes an accelerated observer in a Minkowski background.

What's more, if you consider gravitational perturbations to the metric then the Rindler horizon can be shown to obey dynamical laws analogous to those satisfied by black holes, which are themselves analogous to thermodynamics. (See Bianchi, E. and Satz, A., Mechanical Laws of the Rindler horizon, Phys. Rev D 87 124031.)

 

[Ibix]

Does that mean that if a particle was accelerated at such a high rate would experience the event horizon of a black hole?

No it doesn't, because "acceleration is equivalent to gravity" is an enormous over-simplification of what the equivalence principle means. As ergospherical has noted, there is a thing called a Rindler horizon, but it is only analogous to an event horizon, and it only exists for things that accelerate eternally. It is also behind the accelerating observer, which is to say that the accelerating observer can (if they squint really hard) say that their view of spacetime is similar to that of someone hovering over a black hole, not that they themselves are a black hole. This is essentially the same phenomenon as the impression of added weight in a lift. It feels like an increase in the external force of gravity, not like you are suddenly an asteroid attracting other people in the lift. There is no gravitational attraction caused by the presence of acceleration and no tidal forces - another observer may cross the Rindler horizon and continue to live forever, not fall into a singularity or be torn apart by tidal forces or whatever happens inside a black hole.

 

[PeterDonis]

I will have to find out what a worldline is.

It's a curve in spacetime that describes the history of an object. This is a basic term in relativity.

Due to the 'equivalence principle' which is that to accelerating observers it appears as if spacetime is bent.

No, that's not what the equivalence principle says.

It looks like you need to take some time to learn the basics of relativity from a reliable source. So far it seems like everything you think you know about it is wrong.

 

[PeterDonis]

"acceleration is equivalent to gravity"

Is not even what the OP said. He said "to accelerating observers it appears as if spacetime is bent", which is not even an oversimplification, it's just plain wrong.

 

[PeterDonis]

That's not quite true, but interestingly, it's not a crazy comparison either.

The comparison of a local patch of spacetime near a black hole's horizon to Minkowski spacetime, and of "hovering" observers near the black hole's horizon to Rindler observers, is not crazy--but it also has nothing to do with "spacetime being bent", which is what the OP said. What makes the comparison possible is that within the local patch of spacetime in question, spacetime curvature is negligible. In other words, the comparison depends on the black hole spacetime looking flat (i.e., on the equivalence principle), not on the Rindler spacetime looking curved.

 

[Ibix]

It's a curve in spacetime

Note to the OP: "curve" here is being used in the mathematical sense meaning "a line, not necessarily a straight one". The quoted sentence doesn't mean that spacetime is curved.

 

[ergospherical]

@PeterDonis: that sounds right to me. The other caveat is that the Rindler horizon of an accelerated observer is (by definition) dependent on the chosen observer, whereas the event horizon of a black hole is an intrinsic feature of the spacetime.

And the original premise in the OP is of course physically not correct (obviously you can't form a black hole by accelerating!).

But..., I/A Level side-note, the isometry with Rindler in the patch of spacetime near the horizon is crucial when trying to understand the thermodynamics of black holes, e.g. quantization of a free field --> Bogoliubov transformations between ladder operators for Minkowski & Rindler observers --> Unruh effect.)

 

[Isaac Hart]

Is not even what the OP said. He said "to accelerating observers it appears as if spacetime is bent", which is not even an oversimplification, it's just plain wrong.

This is what the internet is telling me:
Source 1

What is the Equivalence Principle?​

In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein’s observation that the gravitational “force” is experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

source 2

Equivalence principle, the fundamental law of physics that states that gravitational and inertial forces are of a similar nature and often indistinguishable. In the Newtonian form it asserts, in effect, that, within a windowless laboratory freely falling in a uniform gravitational field, experimenters would be unaware that the laboratory is in a state of nonuniform motion. All dynamical experiments yield the same results as obtained in an inertial state of uniform motion unaffected by gravity. This was confirmed to a high degree of precision by an experiment conducted by the Hungarian physicist Roland Eötvös. In Einstein’s version, the principle asserts that in free-fall the effect of gravity is totally abolished in all possible experiments and general relativity reduces to special relativity, as in the inertial state.


Source 3

Very careful experiments have shown that the inertial mass on the left side and gravitational mass on the right side are numerically equal and independent of the material composing the masses. The equivalence principle is the hypothesis that this numerical equality of inertial and gravitational mass is a consequence of their fundamental identity.[1]: 32 
​

"acceleration is equivalent to gravity"

Is not even what the OP said. He said "to accelerating observers it appears as if spacetime is bent", which is not even an oversimplification, it's just plain wrong.

I'm sorry Peter Donis but I think that you may be wrong here, or else perhaps I am lacking in clarity. I do not mean that acceleration and gravity are the same thing, I merely mean that their effect on the curvature of spacetime is similar and in many ways indistinguishable.​

 

[PeterDonis]

This is what the internet is telling me

You gave no links. That's not a valid reference. Neither is "the internet". You need to provide specific links (except that you'll need to do that to me by PM if you want to, since, as you will see below, I am closing this thread). I suspect that even if you provide links, it will turn out that the sources you are using are not good ones. You need to be looking at textbooks or peer-reviewed papers. In your case textbooks would be better since, as I've already said, you need to learn the basics, and that's what textbooks are for. I suggested that in one of your other recent threads; I strongly advise you to act on that suggestion.

That said, none of what you posted supports the claim of yours that you have been told is wrong. None of what you posted says that acceleration bends spacetime, or even that acceleration makes spacetime appear to be bent. The terms "gravity" or "gravitational force" are not the same as "bending of spacetime" (although many pop science sources use sloppy wording that makes it seem like they are the same); spacetime curvature is a more specific aspect of the class of phenomena that fall under the general umbrella of "gravity". So even the (probably not very good) sources you are reading are not saying what you appear to think.

I'm sorry Peter Donis but I think that you may be wrong here

No, I'm not. It only seems to you that I am because you know nothing about the subject, whereas I know a lot. Sorry to be blunt, but I don't see the point of sugar coating things.

There's nothing wrong in itself with knowing nothing about a subject. Many years ago I was in your position: I knew nothing about relativity. I changed that by doing what I have advised you to do: I learned relativity from textbooks. And later on I learned more about it from peer-reviewed papers. I have been doing that for far longer than you have been alive (since you said in a recent thread that you are 15), but I was about your age when I started learning relativity from textbooks (my first one was Taylor & Wheeler's Spacetime Physics, which is still a good one--it has had a new edition since I studied it), so I see no reason why you can't do what I did. And until you do, you are not in a position to even be asking good questions, let alone being able to properly understand the answers. So I really, really think you should go do that before asking more questions.

I do not mean that acceleration and gravity are the same thing, I merely mean that their effect on the curvature of spacetime is similar and in many ways indistinguishable.

And that is wrong. And it is not what any of the sources you posted from are saying.

And with that, the question you asked in the OP has been answered, and this thread is closed. You are welcome to PM me with links to the sources you posted from, and with more questions about them if you like once I have the links.

 

[PeterDonis]

Taylor & Wheeler's Spacetime Physics, which is still a good one--it has had a new edition

And it looks like it is now accessible for free online at LibreTexts:

https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)

Chapter 9 deals specifically with spacetime curvature and what it means.