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Quote from: Mike Gale on 20/02/2017 01:56:17Maybe I misunderstood your concept of a halo. An extended bright object directly behind a black hold does indeed appear as a halo around the black hole. It's called an Einstein ring. An off-axis object appears as an arc, which may be duplicated on the opposite side. This can be interpreted in terms of time dilation, but you can't have it both ways. Light rays are bent towards the black hole if time slows down towards the centre, in which case the background image is stretched outwards. They are deflected away from the black hold if time speeds up towards the centre, in which case the background image is squashed inwards.Light bends away from a BH. There is no energy in a BH from the surface to the center. There is no gravitational dilation within a BH. There is no motion in a BH. Relativity does not work within a BH. Time measurements are severely slowed near a BH as dilation is at its greatest. Light can not reach a BH because light is energy while a BH retains no time energy. It just becomes a mass sucker with no internal motion. Images bend completely around a BH causing the Einstein ring which is the threshold between the BH and fundamental energy.
Maybe I misunderstood your concept of a halo. An extended bright object directly behind a black hold does indeed appear as a halo around the black hole. It's called an Einstein ring. An off-axis object appears as an arc, which may be duplicated on the opposite side. This can be interpreted in terms of time dilation, but you can't have it both ways. Light rays are bent towards the black hole if time slows down towards the centre, in which case the background image is stretched outwards. They are deflected away from the black hold if time speeds up towards the centre, in which case the background image is squashed inwards.
BTW, the mathematical formulation you seek is:ds^2 = A*(cdt)^2 - dr^2 - r^2*d(angle)^2where A is positive and a function of r.I might add that there is no way to reconcile this equality with SR or GR.
The only way A can increase on approach is if gravity is repulsive, as in a white hole.
Variable light speed was not my idea. Einstein wrote about it at length (http://einsteinpapers.press.princeton.edu/vol7-trans/156?highlightText=%22spatially%20variable%22). It just never caught on as a useful way of thinking about GR. Not that it's invalid, he just didn't find it helpful when explaining GR to non-believers. I expect it was hard enough to convince them that the speed of light is invariant in an SR context and chose to let that sleeping dog lie.It's not really fair to say that the SC scaling factor is gravity, although it certainly involves the concept. Gravity is a force whereas the scaling factor represents energy. (A force is the rate of change of energy.) The scaling factor is in fact an expression of conservation of energy for the free fall case. GR theorists cringe at that definition. They contend that it is something completely different and any resemblance to classical concepts like conservation of energy is purely coincidental. I contend that they are confused because they have forgotten to account for SR effects when formulating the metric. But I digress.Splitting gravity into two parts is a new one on me. Can you give me the executive overview or do I have to tackle four more discussion threads?