# Galaxy rotation rates explained without Dark Matter

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your added f brings us back to the problem of adding energy to the system. Which changes the metric tensor via the stress tensor.

We are of course free to change any metric as we like - we can write down any metric and view it as a solution of the Einstein Field Equations by adding the needed energy-momnetum tensor.

Formally that works, the problem is that this matter may not satisfy the energy conditions to be physical (there is a bit of scope here for what we technically mean).

So, the question to Declan is what sort of matter does this solution give us - do we still have a vacuum solution? If not vacuum, then does the matter obey any or some of the energy conditions?

Edited by ajb

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I agree but Delcan has yet to formulate this change.

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Jeez - how many times do I have to explain it?

It is not difficult concept, unless you have a closed mind.

You have not showed there is an error in thinking space time can flow. The coordinate system is not being consumed, just the field within it.

The missing mass is not in the wrong direction - how did you come to that conclusion?

As I have said ad nauseum the reason for inflow is gravitational collapse in a black hole. It won't happen for normal matter as the gravitational energy field surrounding it is in equilibrium and remains essentially static.

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I agree but Delcan has yet to formulate this change.

He stuck an 'f' in there - but right this 'f' needs carefull explanation. (it is a function right?)

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The field your describing contains energy density. Which correlates to mass. Which you have a greater flow toward a BH.

The exact opposite to solving a galaxy rotation curve. You need that added acceleration in the OPPOSITE direction.

Come on this is a simple relationship.

Anyone can simulate greater inflow by increasing the mass of the BH. Thats precisely what f=ma states as a vector.

Your problem is you need that force vector the opposite direction

Edited by Mordred
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It is not difficult concept, unless you have a closed mind.

There are famous last words here!

You have not showed there is an error in thinking space time can flow. The coordinate system is not being consumed, just the field within it.

Right, you have now said that we have some extra gravitational field that is spin-1, right? You last said it had to be a vector field.

As I have said ad nauseum the reason for inflow is gravitational collapse in a black hole. It won't happen for normal matter as the gravitational energy field surrounding it is in equilibrium and remains essentially static.

But as ever, you have not actually shown any of this.

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the mass curve correlation plots an increasing mass density from the centre of a galaxy outward. This is due to the radius element enclosing a greater portion of mass. Distribution of a halo not an isothermal disk profile. That greater mass is the influence of Dark matters contribution to the gravitational potential.

NOT 80% of the Universe

Ever stop to wonder why the NFW profile is a double power law?

Edited by Mordred
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To ajb:

The 'f' is a constant extra amount of curvature of space towards the center of the galaxy - representing the inflow.

Yes, it would be a function of black hole size or diameter. This relationship is unknown at the moment, but could probably be deduced through observations of galaxies.

I didn't say anything about Spin in relation to the gravitational field - I think the notion of spin in this context is not relevant and misleading. There are no particles associated with gravity, so no spin notion is required.

You may have a point about the energy however, as in GR the Einstein Tensor contains the energy of the Gravitational field. If some of this energy is consumed by the BH should it then become part of the Stress-Momentum energy of the BH?

To Mordred:

So you are saying that to explain galaxy rotation rates we need an acceleration AWAY from the center? - that is nonsense.

The acceleration I am talking about is towards the center.

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The 'f' is a constant extra amount of curvature of space towards the center of the galaxy - representing the inflow.

As it is a change in the metric, it leads to a change on the Riemann curvature tensor - this is what you mean?

Yes, it would be a function of black hole size or diameter.

For a given black hole this 'f' does not depend on the coordinates?

Anyway, if it is a constant you can easily show us how it appears in the Riemann curvature tensor. So please do that.

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To Mordred:

So you are saying that to explain galaxy rotation rates we need an acceleration AWAY from the center? - that is nonsense.

The acceleration I am talking about is towards the center.

BINGO and we have a winner. The required mass is in the opposite direction. However acceleration increase in the opposite direction is wrong. The Net acceleration at any given radius must be approximately constant to have a constant velocity curve.

Gravity has spin 2 characteristics. This has been measured via gravity waves.

By the way just how do you believe an increasing acceleration gives a constant velocity?

BASIC math should tell you otherwise.

Edited by Mordred
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To Swansont/Mordred:

Ok, I see what you are saying now - I missed the link to the curve you are talking about in your earlier post.

The curve I was using was the M33 spiral galaxy. It shows the curve flattening out with distance but still climbing as r increases. This curve matches the constant acceleration I am referring to.

Then you should be able to present the analysis of it.

So you are saying that to explain galaxy rotation rates we need an acceleration AWAY from the center? - that is nonsense.

The acceleration I am talking about is towards the center.

A quick inspection of the formula shows that the centripetal acceleration has to decrease with r, as I already showed.

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To ajb:

But the metric g completely determines the curvature of spacetime. This, in turn, defines the connection (Christoffel symbols) - which in turn defines the Riemann curvature tensor.

So by adding the curvature term to g, the Riemann curvature tensor contains the change too.

See the section on 'Curvature' here:

https://en.wikipedia.org/wiki/Metric_tensor_(general_relativity)

To Mordred:

I don't know what you are talking about?

The extra acceleration due to inflow *is* constant with distance, and in the right direction.

Sure, every black hole will gradually increase in size over time as it consumes matter/energy, but this matter/energy will already be contributing to Keplerian gravity even before it is consumed.

As for spin-2, as I already discussed with ajb, gravity is described by a Rank 2 Tensor - sure - but to interpret this as spin-2 is misleading as this is used when treating it as a particle - which it is not.

If you mean the rate of inflow would increase as the BH grows - then I would say this would be quite gradual, and would actually help to explain the observed rotation curve, as it would cause the gradual increase in velocity with distance to flatten out, as the change in inflow would take time to propagate outwards.

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Wow, this is still going on ?

Last I was in this thread I was trying to understand what exactly is flowing into the BH.

It is not space-time as that is a co-ordinate system.

All I got was that its an energy field.

Has this field been further defined ?

And, since it entrains mass ( accelerates it ), is it related to gravity ?

This field seems to be what is at odds with GR according to Declan's claims.

From the quick skim through the last several pages, he claims that his idea is indistinguishable from GR, apart from this energetic field which is continuously being consumed by the BH. The acceleration of this field interacts gravitationally with the mass of the galaxy to produce the observed rotation rates.

But what exactly is this Dark Field ( if he turns out to be right, I want credit for naming it ).

Unless you can define it and provide a way of testing for this field, all you have is GR, with an imaginary part tacked on.

Can you give us your thinking on the field, Declan ?

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Ok - as I have said in previous posts the energy field is the sum of the wave functions of all the quantum particles in the Universe. Every quantum particle is a 3D standing wave that extends to infinity with ever dimishing amplitude. The waves that comprise the particles (and hence the energy field of space) are the most basic form of energy waves - hence the name Energy Field Theory.

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But the metric g completely determines the curvature of spacetime. This, in turn, defines the connection (Christoffel symbols) - which in turn defines the Riemann curvature tensor.

So by adding the curvature term to g, the Riemann curvature tensor contains the change too.

Which is what I said...

See the section on 'Curvature' here:

I am glad you ypu have found this on Wikipedia - but I assure you that you do not need to point me towards such articles for basic information.

Anyay, for fun, show me the Christoffel symbols or the components of the Riemenn curvature for your 'new' metric. It maybe useful for all to see them written out next to the standard ones.

Can you give us your thinking on the field, Declan ?

In truth he cannot... we don't know what values this field takes - or at least he as not really specified this. As he thinks of it as being something to do with wavefunctions I guessed that it must be a section of some (complex) line bundle. But more than that none of us have a clue.

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To ajb:

I don't have the time to familiarize myself with the maths involved in converting the metric to the Christoffel symbols etc at the moment - but I don't need to because the curvature is completely defined by the metric - the rest is just known maths.

I don't know why you keep saying the field is not defined - I already told you the field is the (positive) gravitational potential field. It's value determines the gravitational time dilation & the speed of light, and it's curvature is the same curvature as in GR (except, of course, for the extra curvature of the inflow due to black holes). The energy of the field is represented in the Einstein Tensor, separately from the energy of the 'solid' matter.

Edited by Declan
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But we all know what expanding means. I am still totally lost by your term 'space-time flowing'. What does this mean?

Jumping in here without finishing the thread it could be conceptualized as space time (when thought of as explained) accumulating higher density on approach to the event horizon and aggregating behind it. From what I understand he's saying space time is effected by gravity at an event horizon (special case not sure why) just as particles are. So making it analogous to matter, the flow is simply the attraction of space time to the horizon and it's accumulation behind.

However conceptually this means space time between galaxies would be stretched thin or ripped apart or being constantly created.

Edited by Sorcerer
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I don't have the time to familiarize myself with the maths involved in converting the metric to the Christoffel symbols etc at the moment - but I don't need to because the curvature is completely defined by the metric - the rest is just known maths.

So once again you confess you have no idea of what is involved in physics - this is quite amazing really. You want to had a modification/new interpretation of general relativity but are quite clueless as to what is really needed.

I don't know why you keep saying the field is not defined

You have not defined it carefully enough for anyone to actually work with it.

- I already told you the field is the (positive) gravitational potential field.

This sounds a very Newtonian notion - but lets see.

It's value determines the gravitational time dilation & the speed of light,

Where does it take values? Real or complex numbers, or something else?

How does it determine gravitational time dilation? (Which as I keep saying is not really a universal notion - it makes sense for certian space-times, but not all. )

How does it determine the local speed of light? How is this related to Maxwell's equations?

...and it's curvature is the same curvature as in GR (except, of course, for the extra curvature of the inflow due to black holes).

What is does 'curvature of a field' mean? (I doubt you actually have any idea of what this could mean)

The energy of the field is represented in the Einstein Tensor, separately from the energy of the 'solid' matter.

I don't see how - that is if we understand the Einstein tensor to be build from the metric via the Levi-Civita connection and so on. I agree that you can think of some other tensor fields in a gravity theory, and people have done this. However, the field equations need modification. I cannot see how you can just say that this new field's contribution is through the Einstein tensor - you have to show this.

But then it is clear that your mathematics knowledge here is poor. Don't take that as an insult, but please accept this. If you are really interested in physics then 'get toolded up' - read the books we suggest.

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...accumulating higher density on approach to the event horizon and aggregating behind it.

You need to define density - you could think about the canonical volume associated with the metric, I guess. I have no idea is that is in this context. It is not a tensor field.

From what I understand he's saying space time is effected by gravity at an event horizon (special case not sure why) just as particles are.

Something like that - the claim is that black holes play some special role here.

So making it analogous to matter, the flow is simply the attraction of space time to the horizon and it's accumulation behind..

I think that is the basic idea - but it seems no to make much sense. We need formulate this carefully, this is is where it really come crashing down. And that is before we get on to the physics as Mordred is pointing out none of this seems to help with the dark matter question.

Edited by ajb
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It's funny Declan, I had a similar idea, it essentially tried to have the same effect, the black hole was the source of a modified gravity. My mechanism was gravitational waves exciting the vacuum and prolonging the existence of virtual particle pairs.

Basically we don't need DM or MOND if there's a way for central black holes to spread their influence differently outward over the galaxy.

Mind you, I just have concepts, at least you have some math. DM models have their merits too though, but good on you for trying.

Edited by Sorcerer
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Mind you, I just have concepts, at least you have some math.

Well, in truth unless you have some mathematics you don't really have any concepts. You just have some loose ideas that may or may not be physically reasonable.

Declan's ideas fall into this categeory in my opinion.

The first thing one need to do is be comfortable with the mathematical framework of the physical theories you are working with or working on extending. The does not mean that you have to be a mathematics expert in differential geometry, but you need to at least be able to make calculations and understand the basic language.

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Ajb thinking about the "flow" more carefully it just seemed to be essentially increased stretching/curvature towards and beyond the event hrizon.

Since I only found this conceptually, that's identical to the black hole having some kind of extra mass. The only way there could be flow is from a source, the only source is the center (Lagrange?) point of the nearest black holes. This would be stretched thin to make up for the space curved tighter held beyond the event horizons.

So it seems like an overly complex way of just adding mass to the black holes, in which case it'd be distributed in the wrong way, anyway, right?

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Ajb thinking about the "flow" more carefully it just seemed to be essentially increased stretching/curvature towards and beyond the event hrizon.

How are you defining stretching/curvature?

You want this notion to give you a locally a number than does not depend on the coordinates used. So you need a scalar - there are a few you could choose the Kretschmann scalar. This scalar is useful when working with the Schwarzschild black hole and similar.

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To ajb:

You say:

"You have not defined it carefully enough for anyone to actually work with it."

But the gravitational potential is defined well enough to be used in GR currently. My field is no different - so it can be used readily.

You also say "you confess you have no idea of what is involved in physics". The maths in GR is not the only part of Physics. You said yourself that you are not too familiar with sponsors etc, but I didn't say you have no idea about Physics. It is a big field - even professors don't know everything.

While it would be helpful to understand the GR maths, I don't think it is essential. You don't need to know how a computer works to be able to use it.

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But the gravitational potential is defined well enough to be used in GR currently. My field is no different - so it can be used readily.

Only in the Newtonian limit - otherwise the notion is not really meaningful. So I assume you are working with space-time just in the Newtonian limit? (You have to be clear and careful on this one)

The maths in GR is not the only part of Physics.

So what? Though I will add that basic differential geometry is actually fundamental in almost all (if not all) classical phsyics.

You said yourself that you are not too familiar with sponsors etc, but I didn't say you have no idea about Physics. It is a big field - even professors don't know everything.

You mean with the formulation of GR in terms of spinors and twistors - you are right I am not very familiar with that. But so what? Who claimed that professors know everything?

The point is your knowedge seems to be very lacking in basic aspects of theory that you are trying to work with or extend. I hope you can see this.

While it would be helpful to understand the GR maths, I don't think it is essential.

I disagree. Physics is all about building mathematical models, making predictions of observables and then testing these predictions against nature. While few people today actually work on all of these stages, we are really discussing the model building stage here. Simply put - if you want to work with GR then you need to know what GR is. Right now it seems you do not really know what is involved.

You don't need to know how a computer works to be able to use it.

Sure, but this a poor analogy. If you were trying to build a new and better computer then having some idea of how computers work would be useful.

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How are you defining stretching/curvature?

You want this notion to give you a locally a number than does not depend on the coordinates used. So you need a scalar - there are a few you could choose the Kretschmann scalar. This scalar is useful when working with the Schwarzschild black hole and similar.

Oh I wasn't going to. I was just conceptualizing. Yeah some kind of uniform point distribution which was skewed by its proximity to a SMBH EH. That's a scalar right?

But my point was it seems Declan's idea is just a way of amplifying gravity produced by the special case of BHS and their EHS. It increases the curvature of the entire galaxy, and creates flat spots at the lagrange points between galaxies/SMBH, (or just equidistant points if that type of maths doesnt apply to galaxy/SMBH clusters)

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