Gravitational Time Dilation

Agreed.

 

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The thread was obviously from the beginning a ruse to again discuss BNS, and than later on a further alternative hypothesis by another.

 

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Hi, Raj. Prof. Joshi just got back to me regarding your post on another closed thread, so I'm posting his reply here.

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I agree with Professor Joshi about the analogy for space falling into the hole like a waterfall. There's nothing in the theoretical model that would suggest that. Actually agree with everything he said. I wasn't aware that the photon at r=2M with impact parameter 0 has the possibility to escape to boundary. Thanks for the good post Professor Joshi.

 

Thanks again tashja....
Obviously he confirms the photon heading directly radially away as I have been saying and as also confirmed by Professor Hamilton, but not keen on the water fall/river analogy.
That's more an individual taste thingy, and the Important bit is to realise it is just that...an analogy, and an analogy that has been supported by maths.

 

There isn't anything in the theory to suggest that. For instance the solutions to the field equations are vacuum solutions where the spacetime is static. So the geometry inside the event horizon is fixed. Since we know the actual situation is dynamic the lightlike separation apparent horizon at r=2M moves with any change in M and the geometry [coordinates of the lightlike surface] changes accordingly. None of this suggests that space is falling into the black hole. Space isn't expanding between stuff that is gravitationally bound. You can tell I don't think any science exists to support that particular analogy. Though it's seems to be used a lot.

 

Hi brucep....
Like I said, I see it as a useful analogy, similar to the "inflating balloon" or "raisin loaf" analogies for spacetime expansion.

You're more apt at the mathematical side of things than I, and this is how Professor puts it.......Any comments?
http://jila.colorado.edu/~ajsh/insidebh/waterfall.html
A more insightful way to conceptualize how a black hole works is to picture space as flowing like a waterfall into the black hole. At left is a movie of Boulder Falls that I photographed. Here's the movie with sound.
Imagine light rays, photons, as fishes swimming fiercely in the current. Outside the horizon, space is falling into the black hole at less than the speed of light (or the speed of fishes), and photon-fishes swimming upstream can make way against the flow. At the horizon, space is falling into the black hole at the speed of light. At the horizon a photon-fish swimming directly upstream will just stay there, swimming like crazy, but not going anywhere, the inward flow of space exactly canceling the fish's motion. Inside the horizon, the space waterfall falls faster than the speed of light, carrying everything with it. However hard it tries to swim upstream, the photon-fish inside the horizon is carried by the flow of space inevitably inward to its ultimate fate.

In the image at right, the (happy) fish upstream can make way against the current, but the (sad) fish downstream is swept to the bottom of the waterfall. This picture was drawn by my daughter Wild, and provided the cover image for the June 2008 issue of the American Journal of Physics4.

Doesn't relativity say that nothing can go faster than light? It is true that nothing can travel through space faster than light. However, in general relativity, space itself can do whatever it likes.

The idea of space moving is one that you may have met before in cosmology (the study of the Universe at large), in the notion that the Universe expands.


The Schwarzschild waterfall

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The picture of spacing falling into a black hole has a sound mathematical basis, first discovered in 1921 by the Nobel prize-winner Alvar Gullstrand2, and independently by the French mathematician and politician Paul Painlevé3, who was Prime Minister of France in 1917 and then again in 1925.
It is not necessary to understand the mathematics, but I do want to emphasize that, because the concept of space falling into a black hole is mathematically correct4, inferences drawn from that concept are correct.

The Gullstrand-Painlevé metric is

ds2=−dt2ff+(dr−vdtff)2+r2(dθ2+sin2θdϕ2)
which is just the Schwarzschild metric expressed in a different coordinate system. The free-fall time tff is the proper time experienced by observers who free-fall radially from zero velocity at infinity. The velocity v in the Gullstrand-Painlevé metric equals the Newtonian escape velocity from a spherical mass M
v=−2GMr−−−−−√
with a minus sign because space is falling inward, to smaller radius.
Physically, the Gullstrand-Painlevé metric describes space falling into the Schwarzschild black hole at the Newtonian escape velocity. Outside the horizon, the infall velocity is less than the speed of light. At the horizon, the velocity equals the speed of light. And inside the horizon, the velocity exceeds the speed of light. Technically, the Gullstrand-Painlevé metric encodes not only a metric, but also a complete orthonormal tetrad, a set of four locally inertial axes at each point of the spacetime. The Gullstrand-Painlevé tetrad free-falls through the coordinates at the Newtonian escape velocity.

It is an interesting historical fact that the mathematics of black holes was understood long before the physics. Einstein himself misunderstood how black holes work. He thought that the Schwarzschild geometry had a singularity at its horizon, and that the regions inside and outside the horizon constituted two separate spacetimes. I think that even today research into general relativity is too often dominated by abstract mathematical thinking at the expense of conceptual understanding.
http://jila.colorado.edu/~ajsh/insidebh/waterfall.html


And here is the scientific paper in more precise detail.....
http://arxiv.org/pdf/gr-qc/0411060.pdf

This paper presents an under-appreciated way to conceptualize stationary black holes, which we call the river model. The river model is mathematically sound, yet simple enough that the basic picture can be understood by non-experts. In the river model, space itself flows like a river through a flat background, while objects move through the river according to the rules of special relativity. In a spherical black hole, the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon. Inside the horizon, the river flows inward faster than light, carrying everything with it. We show that the river model works also for rotating (Kerr-Newman) black holes, though with a surprising twist. As in the spherical case, the river of space can be regarded as moving through a flat background. However, the river does not spiral inward, as one might have anticipated, but rather falls inward with no azimuthal swirl at all. Instead, the river has at each point not only a velocity but also a rotation, or twist. That is, the river has a Lorentz structure, characterized by six numbers (velocity and rotation), not just three (velocity). As an object moves through the river, it changes its velocity and rotation in response to tidal changes in the velocity and twist of the river along its path. An explicit expression is given for the river field, a six-component bivector field that encodes the velocity and twist of the river at each point, and that encapsulates all the properties of a stationary rotating black hole.


The Important thing from where I sit/stand, is to understand what is speculative without evidence, as distinct from legitimate scientific theories, and the distinctions and limitations of analogies which are sometimes confused with reality.

 

Thanks, Tashja, and thanks to Dr Prof Joshi.

No Paddoboy, this is false Bravado !! It is not that you proposed this hovering thing and prof Hamilton Confirmed. It is just that you picked it up from Hamilton Website earlier on and then pasted that jila link...You are pursuing this for quite sometime repeatedly and meaninglessly.

And by the way Paddoboy, learn one more thing....The escape velocity at the surface of the earth is around 11.2 Km/Sec....when you throw a stone radially upwards at the speed of 11.2 Km Sec, it does not hover at the surface of the Earth....Similarly the escape velocity at EH (when core is at EH) is c, so ideally even photon should not hover at EH, but of course it cannot get out of BH gravity......But still the above analogy and hovering thingy is given at EH and helps in explaining certain concepts. Why and what ? find out. The answer is not that Earth is not BH...it is much more than that...find out.

 

The waterfall analogy confuses space with spacetime!

The two are not equivalent!

It is a dangerous thing when the lay observer latches onto an analogy intended to convey a limited understanding, of a complex theoretical description.., as an exact wholistic and definitive description. The waterfall analogy is not an exact or complete description of spacetime, let alone an exact description of space.., anywhere!

 

Insightful, OnlyMe...and stated quite well, I might add.

 

Not in the least ol matey, the river model was proposed to me quite a while back, then I discovered the same on Professor Hamiltons web page.
All in all though, and once again, it confines your understandings and proposals to the cesspool once again.

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As I told you before, that is a rather silly analogy for obvious reasons.
But again par for the course for you as usual.
Again, you seem to be floundering somewhat.

 

I totally disagree with your space, spacetime confusion.
Although I will say that what people refer to as space, can be entirely different.
But I see this as pedant.
The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

— Hermann Minkowski, 1908
That's OK...Your entitled to your opinion. Why not though tell Professor Hamilton?
And I see it as far more dangerous when another lay person, derides and dismisses a mathematically validated analogy from a professional.
And obviously as you should know, and as I have stated many times, since it is an analogy, like all analogies, it has limitations, Still it conveys a perfectly valid piece of physics.

 

This single part of your quote, put it out of context when discussing spacetime..., as it relates to GR. Note the 1908... The quote is accurate when discussing SR and a flat spacetime. It becomes debatable and controversial when applied to GR.

Spacetime as it was in SR was 4 space coordinates and 1 time coordinate. Spacetime in GR is not that simple...........

 

It becomes debatable?
SPACE:
PHYSICS) The three-dimensional theater in which things as we know them can exist or in which events can take place. In the Einsteinian worldview, space and time are united inextricably in a spacetime continuum and there is also the possibility of higher dimensions. See also fourth dimension.
Spacetime:
The union of space and time into a four-dimensional whole. More precisely, the inseparable four-dimensional manifold, or combination, which space and time are considered to form in the special and general theories of relativity. In the absence of a gravitational field, spacetime reduces to Minkowski space.

A point in spacetime is known as an event. Each event has four coordinates (x, y, z, t). Just as the x, y, z coordinates of a point depend on the axes being used, so distances and time intervals, which are invariant in Newtonian physics, may depend, in relativistic physics, on the reference frame of an observer; this can lead to bizarre effects such as length contraction and time dilation. A spacetime interval between two events is the invariant quantity analogous to distance in Euclidean space. The spacetime interval s along a curve is defined by the quantity
http://www.daviddarling.info/encyclopedia/S/spacetime.html

You of course mean "3 space coordinates"

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[ but I'm just being picky]
GR differs from SR in that it inlcudes gravity.
Which just happens to be represented geometrically and mathematically by curved spacetime.

 

Then please give the name / affiliation of the person who proposed this river thingy to you, so that due credit can be given to him by Prof Hamilton on this website......thats the honorable thing to do...

PS: I know you have no such names, you are just bluffing...Keep it up.

 

Yes, Yes, it looks silly to ignoramus.

Gravity manifestation is independent of what is Earth or what is BH, but you don't get it, its like river water flowing way above your head.

 

Very good, indeed !! And this forum's verbose warrior member truly demonstrates the danger of latching on to such thingies.

But what took you so much time ? You put it formally only after Prof Joshi clarified on the point.

 

The only bluffing is from you matey, and also your usual effort to get out from under and put the spotlight elsewhere other than your totally error ridden crank nonsense.
Oh, and I certainly do have a name and I have previously mentioned it here also.

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But really, what difference does that make.
Professor Hamilton has mathematically validated the analogy, and that's what counts.
Just as he and half a dozen other experts have invalidated your silly kiddy like BNS, but which you are not adult enough to accept.

Better luck on your next mission.

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Sure I get it. You have been refuted by all the experts and your paper totally invalidated. And I have been instrumental in exposing you for the fraud that you are.