[Mike Gale (OP)]

I'm limiting the analysis to radial motion, but you (jeffryH) may be right. I think Viascience gets his equation of motion for the photon by setting ds=d(angle)=0 so that dr./dt=(1-rs/r)c. That would be the distant reference frame (RF.) His equation of motion for the test mass is based on a series of weak field approximations, which eventually leads back to the Newtonian equation. I'm not clear if he associates that result with the distant RF because he produces an intermediate equation for the local one before converting to radial coordinates and then talks about the Newtonian result like it applies in the local RF. I expect that's a mistake though (either mine or his) because there is no gravitational field in the local RF if you ignore tidal forces. In that case, I am indeed mistaken to invoke the local RF. I would still argue that those approximations don't hold in strong fields so his conclusions about penetration are invalid. Seems like everyone is avoiding the local RF like the plague, but that doesn't seem to stop them from speculating about it.

I'm sure I heard Susskind making the same argument as Viascience. The reasoning seems to be that, if you can convince yourself that the free fall path in the distant RF is approximately Newtonian, it is reasonable to conclude that the local RF is also Newtonian and the test mass floats through the event horizon like it wasn't even there. I contest that line of reasoning because the (Newtonian) speed of the test mass near the horizon approaches and exceeds the apparent speed of light, which itself is approaching zero. SR breaks down when those velocities are the same so we cannot talk sensibly about the test mass beyond that limit.

[JohnDuffield]

So John what are your qualifications? We could compare them to Kip Thorne's.

I have a degree in Computer Science. But my qualifications are not the issue. You don't need qualifications to point to something in the Einstein digital papers. The issue is that Kip Thorne contradicts Einstein.

[JohnDuffield]

I'm limiting the analysis to radial motion, but you (jeffryH) may be right. I think Viascience gets his equation of motion for the photon by setting ds=d(angle)=0 so that dr./dt=(1-rs/r)c...

Remember what Einstein said: "a curvature of rays of light can only occur when the speed of light is spatially variable". This article is worth a read: Is the speed of light everywhere the same? It's by relativist Don Koks, who says this: "If you're fixed to the ceiling, you measure light that is right next to you to travel at c.  And if you're fixed to the floor, you measure light that is right next to you to travel at c.  But if you are on the floor, you maintain that light travels faster than c near the ceiling.  And if you're on the ceiling, you maintain that light travels slower than c near the floor". The vertical light beam speeds up as it ascends from the floor to the ceiling. The vertical light beam emitted just above the event horizon speeds up as it gets away from the black hole. The vertical light beam emitted at the horizon isn't actually emitted because at that location the speed of light is zero. 

PS: black holes can form even when nothing passes through the event horizon. For an analogy imagine you're a water molecule. You alight upon the surface of a hailstone. You can't pass through this surface. Instead you are surrounded and then buried by other water molecules. So the surface can pass through you.

[jeffreyH]

So John what are your qualifications? We could compare them to Kip Thorne's.

I have a degree in Computer Science. But my qualifications are not the issue. You don't need qualifications to point to something in the Einstein digital papers. The issue is that Kip Thorne contradicts Einstein.

Well you are consistently rubbishing professional physicists with far more knowledge of physics then you will ever have. So you can read a set of old papers. Good for you. However things have moved on. General relativity has been verified so your opinion on a set of old notes and letters is redundant. Or you could learn physics. You could start by asking some questions on classical mechanics. There are plenty here that would help you dispel your ignorance.

[jeffreyH]

I'm limiting the analysis to radial motion, but you (jeffryH) may be right. I think Viascience gets his equation of motion for the photon by setting ds=d(angle)=0 so that dr./dt=(1-rs/r)c...

Remember what Einstein said: "a curvature of rays of light can only occur when the speed of light is spatially variable". This article is worth a read: Is the speed of light everywhere the same? It's by relativist Don Koks, who says this: "If you're fixed to the ceiling, you measure light that is right next to you to travel at c.  And if you're fixed to the floor, you measure light that is right next to you to travel at c.  But if you are on the floor, you maintain that light travels faster than c near the ceiling.  And if you're on the ceiling, you maintain that light travels slower than c near the floor". The vertical light beam speeds up as it ascends from the floor to the ceiling. The vertical light beam emitted just above the event horizon speeds up as it gets away from the black hole. The vertical light beam emitted at the horizon isn't actually emitted because at that location the speed of light is zero. 

PS: black holes can form even when nothing passes through the event horizon. For an analogy imagine you're a water molecule. You alight upon the surface of a hailstone. You can't pass through this surface. Instead you are surrounded and then buried by other water molecules. So the surface can pass through you.

Ok so show me the mathematics that backs up the frozen star hypothesis. No running away and dodging the issue John. You act like an expert so give us your workings out. Otherwise you will just make a fool of yourself. AGAIN!

[JohnDuffield]

There's some mathematics in Oppenheimer and Snyder's original paper which you can find here:

  http://journals.aps.org/pr/abstract/10.1103/PhysRev.56.455 .

Note that the Don Kok's article is recent, and that Kip Thorne promotes time travel, which is science fiction as opposed to science.  See this essay by me for further details.

[Mike Gale (OP)]

I'm limiting the analysis to radial motion, but you (jeffryH) may be right. I think Viascience gets his equation of motion for the photon by setting ds=d(angle)=0 so that dr./dt=(1-rs/r)c...

Remember what Einstein said: "a curvature of rays of light can only occur when the speed of light is spatially variable". This article is worth a read: Is the speed of light everywhere the same? It's by relativist Don Koks, who says this: "If you're fixed to the ceiling, you measure light that is right next to you to travel at c.  And if you're fixed to the floor, you measure light that is right next to you to travel at c.  But if you are on the floor, you maintain that light travels faster than c near the ceiling.  And if you're on the ceiling, you maintain that light travels slower than c near the floor". The vertical light beam speeds up as it ascends from the floor to the ceiling. The vertical light beam emitted just above the event horizon speeds up as it gets away from the black hole. The vertical light beam emitted at the horizon isn't actually emitted because at that location the speed of light is zero. 

PS: black holes can form even when nothing passes through the event horizon. For an analogy imagine you're a water molecule. You alight upon the surface of a hailstone. You can't pass through this surface. Instead you are surrounded and then buried by other water molecules. So the surface can pass through you.

The statements you quoted are consistent with what I'm saying, but the idea that you can be overtaken by an expanding horizon is purely speculative. There is no rigorous proof for the viability of that process. Mass can pile up outside the boundary, but it can't cross over unless you invoke QM. Viascience gives a good visualization of that. Remember that the SC solution is a static one. That's one of the reasons you have to keep the test mass small. But again, I should point out that we are straying from the goal of this discussion thread. I'm not really interested in debating the consequences of GR unless they pertain to differences between the old and new metrics. If you want feedback on your other opinions, you should start a new thread. Or if you find this environment too hostile, try commenting on the Viascience videos on YouTube. You will find the author of those (people call him Ozzie) to be knowledgable, responsive and somewhat tolerant of our ignorance. (I think I may have tried his patience by asking too many stupid questions about QM because he has yet to respond to my invite to this thread.)

[PmbPhy]

Don't be offended if I disagree with your opinion.

I'm not. I never understand what people think I'm offended if I say that I don't want to continue discussing something and recommend where they can read and find all of the answers to their questions. I come here to help. People ask questions and I give the answer with an explanation. A lot of the time the person disagrees for one reason or another, e.g. they don't have a solid grasp of the physics and my response. But that doesn't mean that I want to keep trying to help. I've been doing this now for some 20 years. I'm just too tired of lengthy discussions. I help where I can to the extent I choose.

But it never ever means that I'm offended.

[jeffreyH]

There's some mathematics in Oppenheimer and Snyder's original paper which you can find here:

  http://journals.aps.org/pr/abstract/10.1103/PhysRev.56.455 .

Note that the Don Kok's article is recent, and that Kip Thorne promotes time travel, which is science fiction as opposed to science.  See this essay by me for further details.

Well you are pointing to other peoples work and not your own. Your 'essay' contains no original mathematics. Actually no mathematics at all. Anyone can paste together a lot of other people's ideas. In fact that is all you ever do. Like I said try learning some physics. Laziness is just inexcusable for someone criticising those who have done all the hard work and made careers in a difficult field. Hang your head in shame John.

[Mike Gale (OP)]

But it never ever means that I'm offended.

Good to know. I appreciate your input. I thought you were giving me a sarcastic thanks in your last comment. I'll try to read with a more literal eye in the future. However, I didn't find the answers I seek in the references you provided. As far as I can tell, we're breaking new ground with this new metric. What I can't tell is whether it's a better or worse solution. Wilson says it may not be completely rubbish, but it would take a considerable amount of work to find out.

[Mike Gale (OP)]

Here's an interesting result for the radial free fall case (using either metric):
dT/dt=sqrt(a^3+a^2-a)
where: T=proper time, t=coordinate time and 'a' is the ratio of coordinate light speed to proper light speed.

[jeffreyH]

So your a term is similar to the gamma ratio of v^2 / c^2. Except for the coordinate variation of light rather than the speed of a massive particle. Interesting.

[jeffreyH]

Of course this is only applicable for trajectories away from the horizon. When viewed from infinity.

[Mike Gale (OP)]

Of course this is only applicable for trajectories away from the horizon. When viewed from infinity.

Depends on which metric you use:
Old: a=1-rs/r
New: a=(1-rs/2r)^2

[JohnDuffield]

The statements you quoted are consistent with what I'm saying...

Those statements are by Einstein. 

but the idea that you can be overtaken by an expanding horizon is purely speculative. There is no rigorous proof for the viability of that process.

However we have good scientific evidence that black holes exist.

I'm not really interested in debating the consequences of GR...

OK. Sorry I couldn't help.

[Mike Gale (OP)]

I think I got that result wrong. It should be:
dT/dt=sqrt(3a-a^3-1/a)
Can someone check my math?
This expression diverges to infinity at the horizon so I'm pretty sure it's right. It turns imaginary somewhere inside, but you can obtain a real result with the new metric by switching to the alternate signature when a>1. The old metric doesn't make sense anywhere inside because the coordinate speed of light is negative in that case. I expect that's where the purveyors of woo-woo (as Viascience calls them) start waxing philosophical about time travel.
One can presumably derive a similar expression for the orbital case, but I haven't found time to do that yet.

[Mike Gale (OP)]

However we have good scientific evidence that black holes exist.

I don't contest their existence, but the process by which they are presumed to be created by collapsing stars doesn't work without QM. Something has to cross over in order for the horizon to change.

[jeffreyH]

However we have good scientific evidence that black holes exist.

I don't contest their existence, but the process by which they are presumed to be created by collapsing stars doesn't work without QM. Something has to cross over in order for the horizon to change.

In the weak field approximation objects can be thought of as point masses. This does not necessarily hold for a strong field. The horizon can be a function of the instantaneous internal distribution of mass. However this would require that gravitation does not self interact.

[Mike Gale (OP)]

However we have good scientific evidence that black holes exist.

I don't contest their existence, but the process by which they are presumed to be created by collapsing stars doesn't work without QM. Something has to cross over in order for the horizon to change.

In the weak field approximation objects can be thought of as point masses. This does not necessarily hold for a strong field. The horizon can be a function of the instantaneous internal distribution of mass. However this would require that gravitation does not self interact.

I thought about that. It is conceivable that gravity is the interaction between things on the inside with things on the outside. In that case, external objects would not interact with one another except insofar as their own interiors influence the external domain. It's an intriguing idea, but a bit off topic in this context.

[jeffreyH]

If we set T equal to proper time and t equal to coordinate time then we get:
t = gamma(T)

This results in:

t/gamma(T) = 1

Both gamma and coordinate time then vary proportionally which is why I made the statement above. This brings into question the validity of your new metric.