Declan

Never mind. I'm sorry that you cannot see what I am talking about. I am not familiar with the inner workings of the maths of General Relativity as you are, but as I said I am not trying to change that. I have enjoyed some of our discussions, and at times is seemed we were making progress in reaching a common understanding, but we seem to keep coming back to the same misunderstandings. At least I tried to get through to you... Can we stop now?

To ajb: But I'm not trying to change GR, just a metric that is used by it for black holes. My theory doesn't rely on Gm/r for the potential - whatever the shape of the potential field is for a situation described by GR is the same shape for my field too. I am just saying that given a certain value for the potential at a point in space will determine the speed of light and rate of time at that point. To Sorcerer: Good to hear your interest in my idea: Essentially the idea is that a BH has undergone gravitational collapse and so the gravity field around it cannot escape the event horizon either - resulting in the energy field in space being consumed by the black hole too. As it is consumed, the rest of space moves to fill the gap thus setting up a flow of space into the BH. The energy field (a positive potential) is most dense near the BH and drops off with inverse square law as r increases; but the volume of the spherical shell at distance r increases with inverse square law too - so the rate of flow into the BH is essentially constant with distance (unless mid way between to equivalent BHs as you pointed out). Thus orbiting stars in the Galaxy experience an extra centripetal acceleration towards the center of the Galaxy that is essentially constant with distance - thus giving the observed orbital profiles for galaxies. It is not the same as just adding mass to the BH. If the galaxy's motion through space is added into the picture then the observed assymetry in orbital velocities on one side of the Galaxy compared to the other could be explained as the inflow vector of space either adding or subtracting to the galaxy's velocity vector through space.

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.

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.

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.

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.

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.

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.

If you have a laser (i.e. energy in a standing wave between two mirrors) then you suddenly change one mirror to a black body absorber (i.e. black hole) then the existing energy will flow in one direction (inwards) but not be reflected back in the other direction (outwards). The energy of the waves flowing inwards has not changed, but the outward waves have been removed (eaten by the black hole). The effect of the space flowing inwards is a greater effect at, say 20,000 light years from the galaxy center than the Keplerian gravitational acceleration due to mass/energy consumed by the black hole & the black hole getting bigger. Anyhow, the mass/energy eaten by the black hole would already be contributing to the Keplerian gravitational acceleration experienced at 20,000 light years distance even before it is consumed. There would be a change in energy of any matter accelerated relative to the space it is in, but for an already formed galaxy this is already accounted for in the orbital speeds of the stars in stable orbits. When a black hole first forms and space starts to flow the situation is dynamic and there would be some changes to energy distribution. I am concerning myself with the static situation of an already formed Galaxy.

Do you mean the vector addition? If so I posted an example of the vector addition with and without the extra inflow vector (I think it was post #101). I wasn't talking about time dilation, I was referring to the velocity vector of the field associated with moving mass in that case. Where is the added energy? I am just talking about the space field moving. Objects moving through the space field with a higher velocity would mean more energy, but that is what we are talking about: stars that are moving faster through space than expected. So the extra energy is already there in the galaxies we observe.

Which is why I added a constant 'f' term to the Schwartzchild metric to account for the inflow. The inflow is effectively contracting space (divergence) and its effect on an orbiting star is equivalent to a constant acceleration towards the center of the Galaxy. I have another paper on SR that includes a notion of space flow: http://gpcpublishing.com/index.php?journal=gjp&page=article&op=view&path%5B%5D=503

Yes - understood. If normal gravity is the only effect, then there is the missing mass problem. So we can invoke an extra 80% of the Universe to explain the problem, or we can make a small change to the Schwartzchild metric and explain (most) of the problem.

Oh really - sorry, my mistake then... Which post (number) did I give that equation?

I think you meant to type a=v^2/r rather than v=a^2/r. Right? Close to the center shell theorem is required which complicates things a bit. I am mainly referring to the more distant region of r where the main discrepancy exists and the calculation is simpler. There are two effects: (1) the normal gravitational acceleration (keplerian and shell theorem) and (2) the extra acceleration due to inflow which is constant with r as I previously explained. Close to the center the effect (1) will be greatest and the extra acceleration of (2) will only be ~1x10^-11 msec^2 so won't affect it much. I just noticed on the wiki page about Galaxy rotation that there is typically an asymmetry in the orbital speeds on each side of a Galaxy - which would mean that a Dark Matter halo would have to be lopsided in most galaxies to explain the observations! Why would this be? Alternatively if you add the Galaxy's velocity through space to the inflow vector, then this is exactly the sort of result one would expect. On one side of the Galaxy the velocity would add, and other side it would subtract.

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. What type of Galaxy is the curve you posted? There may be more than one effect contributing to the final curve: there could be *some* dark matter, or the flow rate could be dimishing with distance due to space expanding too. It would also depend on the distribution of black holes in the Galaxy. Not every situation in every Galaxy will be the same. I am not in a position to be able to account for the details of each Galaxy. The point is that the effect I am suggesting can account for the bulk of the extra effect required, rather than having to invoke 80% of the mass of the Universe being invisible Dark Matter.

To Swansont: I think you are misunderstanding me: the velocity vector of the inflow doesn't go into the velocity variable of the centripetal acceleration equation, this is the orbital velocity of the star. The inflow velocity represents an apparent acceleration. This is because the inflow is consistently pulling the star towards the centre and changing the star's orbital velocity vector by bending it towards the centre. The rate of inflow is constant with distance from the centre because the field density decreases with inverse square law as we move further from the center, but the volume of the spherical she'll increases by inverse square law as we move further out. The two changes cancel out such that the flow rate is constant with distance. Constant flow rate = constant inward velocity of space = constant apparent centripetal acceleration with distance. To ajb: Ok, if you are thinking in terms of particles - but I am not, and I don't think it is relevant to in the case of gravitation. Ok, so if the curvature is measured relative to standard Cartesian coordinates (a fixed grid) then how is this different to having a fixed grid filled with a field with variable density and the metric describes the curvature of this field? See it is the same as GR.

To ajb: Precisely: compared to Euclidean space, which is effectively a fixed grid coordinate system. A spin-2 representation, maybe, but does it really mean spin-2 in physical terms?

The rank or degree of the tensor is 2 which means it is a two dimensional matrix (4x4). There are 3 spatial dimensions and one time dimension - agreed, space time requires all these dimensions to describe the field (metric). But just because is is rank 2 does not mean it is spin 2. The matrix has nothing to do with spin, unless the word spin has been used to mean rank or degree. There may be other applications where rank 2 tensor a are describing spin, but it seems irrelevant or misleading to say that for the space time metric. So you are saying that any coordinate system can be used at any point in space to suit whatever you are trying to do? What is the curvature measured against if not a fixed grid coordinate system? What is it curving relative to?

To Swansont: But that is what the centripetal acceleration equation and my paper shows. As the flow is constant with distance, it's affect is an extra velocity vector towards the center for every such vector calculation along r from the center outward. This constant extra vector is equivalent to a constant extra centripetal acceleration towards the center. The graph in my paper shows the required orbital speed at each distance r from the center when an extra constant acceleration is applied to objects in orbit around a Galaxy. To ajb: The the gravitational field is just the curvature of space time, what has spin got to do with it? In your opinion in GR is the coordinate system a fixed grid or does the actual coordinate system deform with the curvature of space?

In the field I am describing a black hole will form just as it does in GR. It is simply due the the gradient in the potential increasing past a point of no return for any matter/light/energy (where the event horizon is). Why does the gravitational field have to have a quantum particle associated with it? This is just the view of the Standard Model that says every force has a particle that carries the force. This view is part of the problem - I don't think there are gravitons. Every particle is a structure within the space field. My phone battery is nearly depleted (out of the house at the moment) so I have to stop typing now - more later....

Well it might take analysis of numerous galaxies to work out the equation relating black hole size to rate of inflow. Once this equation is known it would have predictive power to all situations in all galaxies. I would need a supercomputer to model a Galaxy. My main point is that it provides a mechanism to explain the rotation rates without requiring Dark Matter and with only minimal change from existing theory.

Fair point - it was not a good example. The curvature of space is the same in my model. The only un-modeled effect is the inflow affecting black holes. If I make my small change to the Schwartzchild Metric to account for the extra steady inward flow, then use the new metric in GR it should have the desired effect. The amount of the new term would need to be adjusted to a particular rate of inflow for a given galaxy to match the observations.

To Swansont/Mordred: I gave an example of the vector addition that results in the orbital speed in post #101. There is a velocity vector towards the galaxy center due to normal gravitational acceleration (i.e. Gm/r) for a unit time. There is also an additional velocity vector towards the galaxy center due to inflowing space. The two vectors add, thus requiring the orbital velocity to increase in order to maintain the same orbit that would exist if only normal gravitational acceleration was acting. To ajb: An example of a conceptual change is the Earth going around the Sun rather than the Sun going around the earth. The actual numbers in both models are the same, but the earth going around the sun results in a better model. This might not be the best example, but the conceptual change I am suggesting for GR is just in the understanding of what space curvature means: i.e. curvature due to the space-time field changing in density, rather than deforming in actual geometry. The maths capturing the curvature is identical - its just how we think about it that has changed. As the space/energy field can be flowing it would be a vector field rather than scalar. This helps capture other curvature issues such as frame dragging (i.e. Kerr metric etc). Can you explain more about the spin-2 aspect? The real problem with GR may be that the energy of the gravitational field is always assumed to be connected to matter (i.e. it is part of the Einstein Tensor, rather than part of the Stress-Momentum Tensor). Perhaps There should be a version of GR that treats all energy in the system equally.

Well being able to see GR as resulting from a space-filling field is really the only change and is conceptual rather than a mathematical change - however it does allow one to see the situation differently and understand why the Galaxy rotation rates are as they are. This is different to GR as it cannot explain the Galaxy rotation rates. The difference only affects black holes due to gravitational collapse and resulting inflow of the field - for this change I have provided an explanation via the centripetal acceleration equation. It doesn't really require any new or complex maths, although there must be some as-yet unknown equation that relates black hole size to rate of inflow.

The field I am talking about is identical to the Gravitational field and so will be exactly the same as the space described in GR - by definition. The energy in the Gravitational field is not part of the Stress Momentum Tensor. This quote from the wiki page on "Mass in General Relativity": ' "gravitational field energy" is not a part of the energy–momentum tensor; instead, what might be identified as the contribution of the gravitational field to a total energy is part of the Einstein tensor on the other side of Einstein's equation (and, as such, a consequence of these equations' non-linearity).' source : https://en.wikipedia.org/wiki/Mass_in_general_relativity Conceptually, each quantum particle in the Universe is a 3D standing wave that can be thought of as comprising spherical IN and OUT waves that combine to form a standing wave (that satisfies the Classical and Schrodinger wave equations - and so therefore is a stable wave structure). All of these wave functions add together in space (superposition principle) - resulting in a large sum of essentially random wave energy in empty space. In a normal volume of space as much wave energy enters the region as exits it (zero divergence). But In the vicinity of a black hole (the event horizon), waves can flow inwards but not outwards - thus creating a deficit in the energy balance of the space outside of the event horizon. (i.e. move wave energy exits the region than enters it, on the side towards the black hole). Thus the energy field of space begins to flow towards the black hole.