Declan

Yes I have had a look at the metric already and made a suggested modification for field inflow in post #38. It might be better to define the modification to the metric elements for the time (t) and distance ® dimensions as: Originally: 1-2Gm/rc^2 Suggested: 1-(2Gm/rc^2 + f) where f represents a steady inflow independent of distance r. Of course as the black hole grows larger (through consumption of matter) the rate of inflow 'f' would slowly increase over time too.

So the geodesic equation is essentially based on the gravitational acceleration (gradient in the gravitational potential) and determines the metric (i.e. The length, and time taken for light to travel the curved line between two points). It will be exactly the same if calculated for a space filled with a field (medium for light/matter) that is proportional to -phi (i.e. A positive gravitational potential field) that determines the speed of light and rate of time (higher density field = slower speed of light, and slower rate of time). Therefore the GR equations will work in the same way for the energy field I proposed in my Energy Field Theory paper, with the added benefit that space is now viewed as filled with an energy field, and so this field can be consumed by black holes and explain the additional acceleration required to account for Galaxy rotation rates.

Yes that is what is used. What about my other questions?

I don't see any reference to relativistic radiation or cosmological constant, just seems to be based on phi=-Gm/r What about the question I asked about the matrix elements? Is the calculation of the geodesic the only way to derive them? Apart from trying to understand the maths, it seems clear that the line element calculation and the geodesic would be the same for GR based on an energy field with variable density, setting the speed of light and time dilation. A point on your edit: surely if there is *any* difference in gravitational potential between the start and end points there will be a time dilation (however small) otherwise there would be no acceleration.

Hmm the Ryder section on Newtonian limit says the redshift can be calculated from the time-time element of the matrix - this seems to be misleading? Anyhow it seems that one needs to calculate the geodesic equation first in order to know what the matrix elements for the metric should be - is that the only way to do it? What would the matrix elements be for the space around a mass (which is all at the origin)? I guess for a weak field such that phi=Gm/r? In that case no shell theorem required.

I studied matrix maths in high school (up to 3x3 matrices) and was good at it, though I have forgotten some of the details such as which elements to calculate the determinant etc. I am aware of the -+++ +--- convention difference though not the reason why one has to be different from the other three - is it because it is time? Can you explain this easily? When you said 'yes on the distribution' did you mean yes apply shell theorem or yes treat all the mass at the origin? Incidentally the Newtonian limit section says that the gravitational redshift can be derived from the matrix elements due to the equivalence principle, yet this due to time dilation of one gravitational potential relative to another gravitational potential- but you said there is no time dilation in this example. Can you clarify?

I read those wiki pages already yesterday. Is the cloud of plasma extending into space around the origin such that Shell theorem is applied as r changes? Or is the mass being considered as all being at the origin? Either way though, without time dilation shouldn't the element in the matrix for the time dimension just be -1 as it is in normal flat space? This element determines the length of the line element in the time dimension right? So the distance in time between two points would stay the same wouldn't it, as the rate of time is the same everywhere in the space? Or am I misunderstanding the length of the line element for the time dimension: is it the time taken for light to travel along the geodesic between the two points?

So if no time dilation in the Newtonian limit example, what do those two elements in the metric concerning 2*phi etc do? How do they affect the time and r dimensions?

So it seems that the gravitational time dilation formula 1+del(phi)/c^2 appears in the Christoffel symbol in the geodesic equation, and when h00 is calculated and then added to the normal flat space time is becomes the 1+2*phi/c^2 form that appears in the metric tensor. Do you agree? Actually the form in the Christoffel symbol is without the 1+ at the start, that gets added when the normal space is added on. It seems a bit odd that the gravitational time dilation equation doesn't appear in its normal form in the matrix, as the time dimension would be affected by that time dilation factor as a result of the metric, wouldn't it, as that is the effect of the gravitational field on the time dimension. Does some other part of the function modify the result, thus forming the normal time dilation equation in the final result?

Hmmm I'll see what I can find online first... I have not found a very satisfactory answer yet, but two things I found that seem to result in a 2*phi result are: (1) a calculation for the escape velocity in a Newtonian gravity field. (2) the comparison of the GR metric to Newtonian gravity in high gravitational environment where the effect is double the classical result. I remember that originally the equation for the precession of mercury was out by a factor of two - is this in any way similar? From what I can see from the tensor for the Newtonian limit given by Mordred, the factors in the matrix describe the gravitational time dilation affect on the time parameter, and the curvature of space on the next diagonal element in the matrix (in curvilinear coordinates). Is that right? The texts on the Metric just seem to say let g00 = 2*phi but don't explain why...

Ok thanks - I'll have a look soon...

Ok, no problem... Can you point me to a webpage that shows the derivation of the 1+2*phi/c^2 term? I tried to find it in Wikipedia but only found the metric but no derivation of the elements in the matrix...

Ok, I have had a quick look at your web pages - I don't have time to read through fully at the moment. What is the point/question you are trying to make?

Msec^-1 should have been msec^-2 Seeing light from a distant galaxy is not a measure of light's speed. How do we know exactly when it was emitted? In any case if there is Dark Matter the light would take longer to reach us anyhow due to the extra gravitational potential so how could we tell the difference? I'm not quite sure what point you are making in your second point - are you talking about lensing?

To Bignose: The 10^-11 msec^-1 I was referring to was the extra acceleration in spiral galaxies required to explain the orbital velocities that are observed. I was not suggesting the speed of light would be different as measured by any observer in any reference frame. As the speed of light and the rate of time change at the sane time due to the same reason, it will always be measured as c. Any measurements done of the speed of light whilst moving through the space-time medium necessarily involve the signal completing a round-trip so that a timing measurement can be made against the same clock. So any difference in the upstream time as made up for in the downstream time - thus the total time always gives the speed c for light's total travel time. I have shown the maths if this in my paper.

Yes I understood that, but why 1+2*phi/c^2 rather than the GR time dilation formula 1 + delta(phi)/c^2 ?

To ajb: Why can't you trust it - it is simple maths to follow? To Mordred: Getting back to the line element for the gravitational field: where does the 1+2*phi/c^2 term come from. I know it is to do with the gravitational potential, but can you please explain it? Thanks...

Ok, sure - up to n dimensions. To Swansont: Yes, but given the extra acceleration is only in the order of 1x10^-11 the flow rate would be quite low. Anyhow if Dark Matter exists it would slow the rate at which light takes to escape the Galaxy too due to the extra gravitational potential (which I guess in GR terms would mean the creation of extra space that the light would have to travel through). The Michelson Morley experiment is not a valid test for an aether due to the length contraction of all the apparatus in the direction of movement through the aether. I show this to be the case in my paper.

I just read through the wiki on line elements. Why didn't you just tell me that it is Pythagorous theorem in 4D? Apart from the confusing symbols used, the tensor is effectively just calculating the line length given 4 dimensions of minute length changes. (At least for normal space time). I guess when space is curved then the 4 different minute lengths will be slightly different - giving a different total length. Does this sound about right?

Ok - how confusing, but never mind... So Can you explain (in words) what the full equation is saying? For example: The light distance between two events on a 2D sphere = ??? - ??? - The volume of a spherical shell at radius r

Ok, so does that mean that ds^2 is a distance in meters? Why not just say 'd' or is the s^2 a reference to 2D space? If so it is very confusing having ^2 mean different things in different parts of the equation. Or is it simply the line element's length (distance) squared?

When you say "the physical distance of objects in the gravitational field", do you mean the distance between objects based on how long light takes to travel between them? i.e. the space's size expands near massive objects, causing light to have to travel further to get to the other object. what is ds^2 again? What does the term "line element" mean?

In my comment I was talking about qualitative understanding (i.e. understanding the principles, rather than the numbers). However, now may be a good time to help me understand the maths that you are familiar with. I sort of understand the example you have given, correct me if I am wrong: - you are taking a density of matter in a region of space D and integrating it over that area to get a total mass M, which is at the Origin. - Then you are showing the change in position of a test particle due to this mass M? Or is it indicating how far away the two particles are (in a variable geometry space)? A couple of questions: (1) What is the N subscript on the Potential? (2) Why is there no time variable? (3) I have seen the Omega symbol elsewhere - it expands to another formula doesn't it? Can you explain the Omega to me? And also the ds^2, is that the double differential of distance (i.e. the acceleration of the test particle)?

Here we go again... To Swansont: How can we test for an Aether?

To ajb: I didn't say we don't need Tensors, I said it is possible to understand Relativity without getting involved with the Tensor maths. I can explain exactly how Time Dilation, Length Contraction and Mass Increase works without involving any Tensors. It is also to understand qualitatively how GR works without knowing how to do the Tensor maths. The Tensor maths is a neat mathematical tool for doing exact calculations on the non-linear equations governing the motions of test particles within space-time - agreed. To Strange: Accepting that the speed of light is not constant is not a complete rejection of GR - not at all - even though the constancy of the speed of light was Einstein's first assumption that led him to Relativity, the whole theory remains essentially intact by allowing light's speed to change (along with the rate of time) and have a space-filling field with variable density. To MigL: It's not the coordinate system that disappears - it is the energy field that fills the coordinate system that disappears. And when we say 'disappears' it is in the same sense as normal matter disappearing into a black hole (where is the source of normal matter in the Universe). Both the matter and the energy field (which are essentially the same thing anyhow) become part of the black hole. The black hole may eventually evaporate (via hawking radiation) and release the matter/energy back into the Universe anyhow - so nothing lost forever. To Mordred: I wouldn't mind leaving the thread open and try to understand GR Tensor maths a bit better so that we can have a more meaningful discussion on this (if I can find the time to understand it). I still think it should be possible to move past the sticking point of Tensor maths and discuss the idea whilst acknowledging that this is an area that needs to be worked on. To ajb: In above comment: "it is also to understand" should read "it is also possible to understand".