# (Alpha) General relativity is self-inconsistent v2

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Anyone interested in this discussion should probably run their eye over all the related threads, especially the last one:

Guest254: No problem, I have a pretty thick skin, and I don't hide the fact that my comments are made from the layman's perspective. Maybe you could explain in layman's terms how, inside its horizon, the math shows that a black hole accelerates matter at a rate > c? My resolution to this is that matter does not actually cross the horizon, ever. Call it a "throw away" comment if you wish but I'm willing to bet I'm not the first person in the world to think of it.

My resolution to this is that matter does not actually cross the horizon, ever. Call it a "throw away" comment if you wish but I'm willing to bet I'm not the first person in the world to think of it.

No, you're not. It's a common misinterpretation, that I've read at least twice before on internet discussion fora.

The first question is, in whose frame does matter not actually cross the horizon?

...the math shows that a black hole accelerates matter at a rate > c?

Does it? Are you sure about that?

Maybe you could explain in layman's terms how, inside its horizon, the math shows that a black hole accelerates matter at a rate > c?
The mathematics of general relativity doesn't say that at all. The issue here is with frames of reference: for instance when you're inside the even horizon there's no such thing as a stationary observer so care must be taken.

However, I would be willing to go through the ins and outs of it all if you'd be willing to meet me half way. If you make the effort to learn a little GR (i.e. just the basics, so you can look at geodesic motion of test particles in the Schwarzschild spacetime), I will outline how the mathematics translates into physics.

Ben, I would consider arriving at a "common misinterpretation" > "throw away comment" so thanks

I assume you're going to mention the fact that, from the frame of the person crossing the horizon, time passes normally. If it were possible to do so, I imagine this would be true. BUT, imagine the rest of the Universe as calculated from that same frame - it would speed up as the horizon was approached, faster and faster until INFINITY had gone by. I'm not sure what that even means, except the fact that we can be pretty sure that it cannot happen practically.

Another issue is this: just because we can calculate the size of black hole needed to avoid spaghettification does NOT mean we understand what happens to the non-zero mass objects that are approaching the speed of light (and beyond!). If Zanket wanted to rest his entire argument on this point alone I would give it more credence, but this is exactly why I said in post 16 that if there exists a contradiction between our knowledge of black holes and our knowledge of GR, my vote would be that our knowledge of black holes in incomplete.

I have another theory as well, which relates the calculation of moving FTL with traveling backwards in time. If this were true, and if it were also true that just below the horizon objects are being accelerated > c, then one can imagine all matter being "stuck in time" on the horizon.

Guest254, you got it, I'll do some research and come back.

Ok, I'm going to have a rant.

RJBerry, you are attempting to make claims and predictions about one of the most complicated theories of physics there is. You don't know any GR other than that which is written in pop science books, yet you seem to think this provides you with enough knowledge to make claims and conjectures about said theory. Looking at things as complex and bewildering as black holes requires one to study the details, in depth. And in GR, details means maths, and tough maths at that. It is utterly naive, and a little arrogant, to believe that you shouldn't have to jump through the same hoops as everyone else. People such as yourself seem to want to drop flashy lines about "quarks, black holes, event horizons...", but aren't willing to put in a little effort and get your hands dirty.

I implore you, learn a little humility and go back to the basics. Go through a book on classical mechanics, then on special relativity, then on quantum mechanics, then look at some GR. You will find these sorts of conversations much, much more enjoyable if you could add a little more than a vague armwave and a word salad. The more you put into learning the physics, the more you'll get back. I'm sure all the people on this forum would be more than happy to help you through exercises in text books and help you through all the stages of the aforementioned topics.

Your example involves a particle at r=2m and another at r=2m+e. Immediately alarm bells go off in my head because while you can construct inertial frames iin this situation, you can only do them locally, not of arbitrary size and you'll find that in any region larger than a point you get differences from SR, since space-time curvature is non-zero. You seem to be trying to construct arbitrarily large frames, which are not going to be true for anything more than an instant (so motion of the particles cannot be considered).

Guest254: Not the first time I've been accused of arrogance, but I was sincere when I said I would do some research to learn more about black holes. I'm not looking to pick a fight on this subject because I am UNARMED. What little knowledge I do have came from high school physics, and is basically represented by the picture below. The simple high school math does in fact show that inside the event horizon the accelerative forces exceed c. Whether you want to deal with this apparent paradox by saying that stationary frames do not exist within the horizon, or if you want to say that space is stretched outside the horizon while time is stretched inside the horizon, fine, but right now neither of those explanations mean anything to me until I learn more. I said I would try to learn so why the rant?

While I'm busy learning, please explain how SR concludes that no matter can ever be accelerated to c without an increase in mass to infinity while at the same time GR claims that a subject can effortlessly cross the horizon of a sufficiently large black hole? I'm sure there is an answer but you can forgive me for identifying this issue within the context of my limited education on the subject.

SR is a local theory, except when your space-time is flat everywhere. In SR you have a space-time with SO(3,1) symmetry everywhere, because any inertial frame you pick is as big as you like, it's valid over all the space-time. Throw in gravity and you still have SO(3,1) symmetry at points. You can do Lorentz transformations but all inertial frames are only as big/valid as the region they inhabit which has no space-time curvature. The bigger the space-time curvature the smaller the region you can hold SR as even an approximate theory. Why would anyone expect SR symmetries to apply over large regions of space-time near a black hole? It explicitly requires gravity isn't there so saying "Gravity isn't there" when you're standing next to a black hole is a flawed assumption to make, unless you work over a very very small region. As you get closer to black hole event horizons this region gets smaller and smaller. When you are inside the event horizon there are no real inertial frames because, as Guest says, everything MUST be moving, you cannot use a Lorentz boost to put you into a stationary position.

Berry, all I see you do is make claims about theories you don't know about. QM, SR and now GR. Put a sock in it.

Whether you want to deal with this apparent paradox by saying...
It's not a case of "dealing with a paradox", there is no paradox. There is only your misunderstanding of black hole dynamics, based upon your complete lack of GR knowledge. Let me give you an indication of what your posts read like.

"I don't like the structure of the Chinese language...", or "I think this Chinese person has misspelt something...", or "I think the Chinese language evolved from...".

"How much Chinese do you know...."

"I know how to count to 3 in Chinese, that's it".

Your actions are not uncommon - it seems quite a few people seem to take part in this sort of behaviour. I blame wikipedia.

While I'm busy learning, please explain how SR concludes that no matter can ever be accelerated to c without an increase in mass to infinity...

I'll stop you right there. In SR mass is a Lorentz invariant, and as such does not change as speed increases, your statement is wrong.

Wow Alpha I feel conflicted; on one hand you clarified to me that SR only holds in the absence of a gravity field - that makes sense. On the other hand you are rude...:bravo:

<edit: I've decided that if I go on the offensive I will lose my opportunity to ask follow ups >

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Prometheus: it's invariant mass (aka rest mass) which is Lorentz invariant (hence the name). The relativistic mass includes the kinetic energy of the body and is NOT Lorentz invariant.

Guest: "paradox" means something that is true but at first glace appears to be false. "Apparent paradox", as I use the term, means that it is a presumptive paradox to me, expecting that to others it is quite clear that it should be the case. I'm not claiming that "Physics is wrong".

AlphaNumeric said:
When you are inside the event horizon there are no real inertial frames because, as Guest says, everything MUST be moving, you cannot use a Lorentz boost to put you into a stationary position.

When we say that no real inertial frames are possible inside the event horizon isn't it simply because there is no acceleration such that the inertial frame may exist? I'm having a problem understanding how that is different from saying that inside the horizon accelerative forces are > c.

Mod Note:

AN is not rude, he just doesn't tolerate bullshit.

One must be careful to tell the difference, otherwise one may find that most physicists are rude''.

BenTheMan, I guess if you or AlphaNumeric define "bullshit" as me asking questions about Physics on a Physics forum to enhance my understanding then I have a lot more bullshit for you. I would also call into question your role as a legitimate moderator if you truly have this attitude.

Prometheus: it's invariant mass (aka rest mass) which is Lorentz invariant (hence the name). The relativistic mass includes the kinetic energy of the body and is NOT Lorentz invariant.

I'm going to chew the fat with you on this. Relativistic mass is not a mass. It's simply another expression for the energy of the system. Let me ask you a question: What is the mass of an electron? is it $$m_e$$ or is it some function of the electrons energy? It can't be both - why would we have two definitions of the same thing?

Calling relativistic mass a mass is pointless and confusing, and also wrong.

Prometheus: I guess the answer to your question depends on what kind of mass you're asking about. The fact is that there exists more than one definition for mass. Why would we have two definitions of the same thing? I don't know, I didn't name them.

I was under the assumption that relativistic mass would approach infinity as the horizon was approached. My confusion was in how this "infinite" relativistic mass would be expressed (in terms of infinite energy, or infinite gravitational attraction, etc). I'm wondering now if the problem is somehow resolved because of the curvature of spacetime caused by the black hole, per AlphaNumeric, but I'm still having a problem internalizing what that means.

Wow Alpha I feel conflicted; on one hand you clarified to me that SR only holds in the absence of a gravity field - that makes sense.
No, I didn't say that. GR has SR as a subtheory and not just in the sense of having SR as a zero mass/energy limit. In regions of low curvature you have that a space looks like Minkowski, so while in SR two objects which are seperated by huge distances can be analysed in the same inertial frame, that isn't true in GR, with the deviation from SR description being related to the amount of curvature in the region.

But that then means that you can always have SR symmetry at a point in GR, irrespective of the amount of curvature at that point (other than infinite, obviously). Mathematically this is equivalent to saying the metric is preserved by Lorentz transformations. Infact, this defines the Lorentz transform group in terms of the Minkowski metric, $$\Lambda \eta \Lambda = \eta$$. If GR has Lorentz symmetry then $$\Lambda g \Lambda = g$$. I don't have the time or want to type the proof it does, look up 'vierbeins'.

Of course if you looked at books before shooting your mouth off, we'd not have this discussion and you'd be much more knowledgable about relativity than you currently are.
On the other hand you are rude...:bravo:
I'm blunt. But I am not a liar. So while my criticism/comments might be unpleasant they are, none-the-less, close to the mark.

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