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.