Translational Motion of Black Hole

No, GR is a field theory, that means, its basic equation, the Einstein equation, is an equation on how the gravitational field changes, moves. It is not like Newtonian theory, where the sources of the field define the field, and the field cannot change without the sources changing. The field changes following the field equations. The analogy is the EM field, which also has, with Maxwell, own equations, and changes following these equations.

Of course, moving sources also lead to modifications of the field - for EM as well as gravity. But, in above cases, this influence is bounded by the speed of light. Thus, only the body before reaching the EH can influence the gravitational field outside.

 

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This would be relevant if we are talking about non-uniform motion of 'BH'. But that implies it forms part of typically a binary system. Post #1 reads like simple rectilinear relative motion. Maybe Rajesh needs to tighten things up and be more specific.

 

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If we discuss black holes and the spacetime inside of an event horizon strictly within the context of GR, we are exploring predictions about a spacetime that is outside of our ability to explore and/or observe. It is like discussing the twin paradox in SR.., where the required conditions involving velocities and time are physically impossible, and yet accepted within a hypothetical... Most of the expert comments about black holes either by email or by link to an external source are explaining and/or speculating about some aspect of GR the theory. Expert comments in some past threads when confronted with the questions about singularities and communication issue across event horizons, have implied or sometimes specifically replied by admitting that, point singularities do not exist in reality and intuitively the mass of a black hole must communicate with the spacetime outside of an event horizon... Sometimes these qualifications include a reference to the hope that some future QTG will provide a better understanding.

Experts acknowledge that without some fundamental understanding of gravitation (not provided by GR), some of the predictions of GR, as they relate to black holes.., are not consistent with any classical experience. Intuition and logic tell us something is missing in our understanding of the fundamental nature and origin of gravity, that we hope will be answered by some future QTG.

Still cosmologists and theorists assign physical characteristics like mass and angular momentum to black holes. The SMBHs at the centers of galaxies are not described as fossil fields, they are described in terms of billions of solar masses...

The point is that these discussions are usually exploring attempts to place purely theoretical predictions into some context comparable with classical experience. Science and theory have not yet connected those dots.

One thing that appears certain is that there is, at present.., no entirely satisfactory answer, that is consistent with intuition, classical experience and theory, to the questions in the OP. The Fossil field is an attempt (staying within the context of GR), to explain how the gravitational field of a black hole can persist, even after the initial mass has fallen beyond an event horizon, that prevents further communication across the event horizon. But it is not supported by observation and experience. It depends on accepting the predicted theoretical limitations....

What I keep attempting to say is that we will not find the answers by limiting the discussion to GR. Nor can we expect that the answer will be found through some application of classical experience and/or intuition alone.

The Gravstar is perhaps the closest possibility, but it has its own limitations and does not seem on close examination, to be a viable answer... At least within the context of our current understanding of physics.

Which leads once more to some variation of a QTG, which so far has had no real success. However, since at least some of the experts have presented some future QTG as where the answers should be discovered, it seems that is where these discussions should be focused... But we have no experts on any QTG to help guide the way.

 

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Q-reeus, without saying I believe the following is the case...

Perhaps what is at issue in the OP, is a paradox introduced by the idea that there is a mass inside an event horizon that cannot communicate any associated gravitational field across that horizon.., and the idea that the external field is a fossil field.... If the mass inside the event horizon moves and that motion cannot be communicated across the event horizon.., the fossil field and the black hole could not be connected... You wind up with something like a fossil filed and a fossil event horizon, which are connected to the universe as a whole.., and a black hole and its event horizon, that are no longer connected to any external spacetime...

Once the black hole forms, any relative motion of the black hole becomes fixed and unchanging. However, the fossil field and its fossil event horizon are still connected to spacetime and other gravitational fields and so are subject to changes in their state of motion...

 

Well OnlyMe, maybe the OP had such a scenario in mind but it's not my reading of it - the title more or less gave the lead imo. However, if Rajesh really meant internal motions that somehow were able to be other than spherically symmetric wrt overall center of mass, I'm out of it. It would then degenerate into a continuation of past bickering over what 'inside an EH' could sensibly mean. There are formal GR positions that seemingly make sense if cast using e.g. Kruskal-Szekeres chart. And of course lately a push to eliminate the need via avante-garde notions like 'firewalls' or 'fireworks' or... stay tuned.

Even for voiolently accelerated motions like inspiralling binary system, there supposedly are self-consistent numerical GR simulations up to the final merger event. But not afaik delving deeper than the EH region. If you have faith in such, well and good I suppose.

 

Maybe the OP wanted to leave the things simple enough for himself and that's why has considered only the simple case of translations. I would prefer more turbulent scenarios: Take two old black holes which do not rotate. Shoot them close enough to each other, so that they have to form a single BH, but a little bit skew so that this BH rotates. If the old enough BHs have "already" formed a singularity, we would have to observe, inside, the focus how two point singularities start to create a ring singularity. I would expect this to be quite funny.

 

I refer you to previous answers:
Fossil fields, nonlinearity and the legitimacy of all frames of references, overcomes any and all problems you seem to visualise.
BHs are no different gravitationally than an ordinary object of equal mass. It's only when an object gets very close that BHs behave differently.

On another note, this thread actually seems to be a rehash of previous threads that have been closed, and also others of yours that have operated under the guise of a question, while in actual fact being an excuse to again push an already invalidated alternative hypothesis.
Both contravene rules.

 

Other than the unlikelyhood that any BH is really Schwarzchild metric, as all would be born already with angular momentum, I cannot see any problem with your "thought" scenario of point singularities spinning up to ring singularities.
Also worth noting most mainstream cosmologists and physicists do not believe any point singularity exists due primarily to the infinities that are related.

 

I probably did not present that well, but it is not of any importance unless Rajesh decides to clarify just what he intended.

 

The gravitational field is the g field and it's infinite in extent. It's the tidal field that gravitational waves propagate. It's dynamic.
g_Newton = M/r^2

g_Schwarzschild = gamma M/r^2

g_rain = M/r^2

If M remains constant during the gravitational collapse then g will remain constant over all r during the gravitational collapse. All r outside and inside any light-like boundary. The lightlike boundary is irrelevant to the value of g. This is really simple. g varies with changes in M and r. Inside and outside a black hole.

 

I also do not (yet) see a problem. That's why I wrote "I would expect this to be quite funny".

Maybe there could appear some problems for some concepts.

 

For those who, like me, have more than occasionally raged against the omnipresent spectre of Euclid and ancient Greece in physics, I have found and read material from a kindred spirit and an authority on the subject who has taught physics at the Univerity of Pittsburg for decades. His online reference on the differences between Galilean and Einstein-Lorentz transformations are a thorough and thoughtful treatment of the subject I have not found elsewhere. His two step derivation of E=mc^2 is there also (in the online book), is the best I've ever seen, and lacking in no mathematical or physical rigour. He is easy to find. Just google John D Norton.

Coordinate systems like those origins nailed to the center of a BH don't mean very much when the black hole itself begins (or continues) to move. You can't find the center again without reference to something even bigger, and those are likely to be moving also.

The principle of relativity, if applied properly, must, like those turtles the woman who heckled one of Bertrand Russell's lectures mentioned, go "all the way down", which is to say, if you make any assumptions about any quantum field(s) that are either moving at c or at rest, they must do so relative to something else. A minimum of two such fields would be required; one that is at rest relative to virtual particles created in the vacuum, and one that is moving at c relative to the one that is at rest, at every point in space, in every possible direction. There is nothing like an aether nor an aether wind implied in this concept that might be used to nail one of those blessed ancient Greek coordinate systems to. Neither is there a quantum field that moves at any speed that falls between the limits of 'at rest' and c, which is the region of this universe we inhabit.

Not two turtles. A turtle and a hare, and they aren't standing (or running) on a Euclidean sold. Apologies to Aesop.

It is that "something else" they either stand or run on which confounds folks who are still doing physics and math as though they were still doing so in ancient Greece. Their minds are as solid (in the sense of being set in concrete and rebar) as their ancient geometry.

 

As is usual with your musings, I am left confused as to your actual pov and argument. But let's be clear on one thing wrt bold text above. Owing to the 1/r^4 power spectrum law that e.g. vacuum EM field fluctuations exhibit, the vacuum is strictly Lorentz invariant. Hence it's impossible to 'be at rest relative to virtual particles'. There is simply an invariant spectrum - whatever one's relative speed.

One extra thing - in #13 (and following) I neglected to mention that in the case of gravity, a Lorentz boost acts on mass M (gravitational 'charge'), unlike say for electric charge which is a Lorentz invariant. Otherwise, the similarities hold.

 

This is a very generalist definition of EH as stated in wiki........

......In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer......

Although we will restrict our discussion to classic BH only, but to understand OP better we may refer that a BH can have 3 - Parameters that is Spin (Angular Momentum and thus frame dragging), Charge (Electro Magnetic Field) and Mass (Gravitational Filed). Prevalent mainstream theory assigns angular momentum and Electro Magnetic field with the spacetime > 2M (Outside EH), not with spacetime inisde EH (r<2M). But there is a special treatment given to Gravity, the g filed is assigned till r = 0, its kind of, for gravity manifestation there is no EH restriction. As per theory this is true that gravity manifests (from r = 0+ onwards) as if an ordinary mass M is present at r = 0. But same treatment is not given to Angular Momentum and Electro magnetic field, they are assigned to filed outside EH, which practically has no connect with things inside EH....in fact both side are temporally (time like) disconnect.

[Take a crude analogy, we go to a high security complex, leave our mobile phones (Electromagnetic Field) and Headgear (Say Angular Momentum) outside the premises (>EH), and enter the complex (BH). Now the security complex moves, which is isolated from outside, so how our mobile phones and Headgear move in sync with complex?]

So, the paradox, is how the properties of BH assigned to spacetime outside EH, moves along with the BH ? There is absolutely no need to invoke relative motion and various transformations here, the point is a BH moves.

PS: 1. This issue will not arise, if we settle for any object > EH.
2. This issue will not arise if we assign all the properties to singularity, naked singularity, without assigning any
relevance to EH.
3. OnlyMe reference to prof (as taken in quote by me earlier) also appears to contradict the basic tenant of BH,
which states that Gravitational field is present from r = 0+ to r = infinity as coolly as it could. Because if the
mass would manifest only at > EH, then we will not have extremely curved spacetime inside EH.
4. This paradox can be solved, if somehow we can prove that Gravity has the power to drag Electromagnetic
field and angular momentum field along with it.

 

Time literally stops at the EHof a BH, and can be said to actually change places with space within....
http://www.einstein-online.info/spotlights/changing_places

How are we able to postulate something which is shown to be totally false?
Neither time and space are absolute, and in the case of time, this has been totally evidenced and supported by many observations.
http://everythingforever.com/einstein.htm

GR is not an ideology.
An ideology is a set of opinions or beliefs of a group or an individual. Very often ideology refers to a set of political beliefs or a set of ideas that characterize a particular culture. Capitalism, communism, socialism, and Marxism are ideologies. [WIKI]
GR is a total legitimate scientific theory in the category of near certain and supported by overwhelming evidence.
It of course does have limitations where it is non applicable, and that obviously is that the quantum level.

? Why would the light cone become uncertain?
Any future validated QGT would most likely and as a necessity invoke classical GR at that limit, and also just as necessary obey Newton's laws at that level.

 

I get a funny(?) idea from this, may be you are also thinking on the same line....

If Gravity can be manifested without any actual whereabouts of mass and its distribution (like BH, mass is undetectable but Gravity is present), then our Dark matter thingie is resolved. We can always say that so and so visible mass was present and now it has disappeared with some distribution (a la special BH type animal) leaving behind the Gravitational Field. No need to hypothesize that ever elusive monster called Dark Matter.

PS: This post is pure and pure fun oriented speculation, not to cause any coronary disturbances.

 

gamma is a problem inside EH !!

 

Can't argue with that.

Or to put simply, a BH can have three properties, mass, charge and Spin.

If I understand you correctly, that has been rejected by a few experts in past threads.
If we observe frame dragging, we are reasonably and logically allowed to infer that also spacetime and the mass is also spinning within the EH. Even though information inside the EH is unobtainable, GR does predict total collapse to the classical point singularity. GR breaks down at the quantum/Planck level and most scientists do not believe that the point singularity will be reached, with its absurd infinite quantities.....

I don't see a paradox existing at all.
If the BH moves, so to do the properties of the BH, as they also are properties of the curved spacetime within the EH, and of course nonlinearity and the fossil field takes care of your paradox.

Again, no paradox. Just as the Earth and Sun drag their gravitational field and EMF along with them, considering the fossil field and nonlinearity, the spacetime that makes up the BH and the mass that gives it its critical curvature, will also move along with it.

 

You must have been in quite a hilarious mood, posting this. L(initial) = 0, L(Final) = Non Zero.....Its great that one of the poster took this 'Onion' post of yours very seriously. You proved something.

 

Not at all.
How do you explain for starters the bullet cluster findings......
Dark matter and normal matter have been wrenched apart by the tremendous collision of two large clusters of galaxies. The discovery, using NASA's Chandra X-ray Observatory and other telescopes, gives direct evidence for the existence of dark matter.

NASA Finds Direct Proof of Dark Matter
For Release: August 21, 2006

NASA RELEASE 06-297

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X-ray/Optical Composite of 1E 0657-56
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http://chandra.harvard.edu/press/06_releases/press_082106.html