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The River Model Of Black Holes

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Posted by Richard Ruquist on November 15, 2004 15:49:06 UTC

Some time ago on this forum I presented the opinion that space must be flowing into black holes at the speed of light at the event horizon for light to be trapped inside of the horizon. That idea was ridiculed by some other physicists who contribute to this forum. But now a paper claiming exactly this has been published. Specifically to quote from its abstract, which is copied in full below:

"the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon."

Here is the link:

and the Abstract:

The river model of black holes
Authors: Andrew J. S. Hamilton, Jason P. Lisle (JILA, U. Colorado)
Comments: 14 pages, 4 figures


There is a companion paper cited below. It is much more detailed, and claims to resolve the invalid prediction that for non-rotating spherical Black Holes, the inflowing river re-expands into another universe...that is, it is a white hole.

I could not determine for the paper below just why the white hole is not allowed. But I did find one comment very interesting. The comment is that the tidal forces of supermassive black holes are much smaller than a stellar size black hole.

With Steller black holes, tidal forces would rip yop apart long before passing through the event horizon. But with supermassive black holes, you can go well beyond the event horizon without harm.

Inside charged black holes I. Baryons
Authors: Andrew J. S. Hamilton, Scott E. Pollack (JILA, U. Colorado)
Comments: 31 pages, 12 figures

An extensive investigation is made of the interior structure of self-similar accreting charged black holes. In this, the first of two papers, the black hole is assumed to accrete a charged, electrically conducting, relativistic baryonic fluid. The mass and charge of the black hole are generated self-consistently by the accreted material. The accreted baryonic fluid undergoes one of two possible fates: either it plunges directly to the spacelike singularity at zero radius, or else it drops through the Cauchy horizon. The baryons fall directly to the singularity if the conductivity either exceeds a certain continuum threshold k_oo, or else equals one of an infinite spectrum k_n of discrete values. Between the discrete values k_n, the solution is characterized by the number of times that the baryonic fluid cycles between ingoing and outgoing. If the conductivity is at the continuum threshold k_oo, then the solution cycles repeatedly between ingoing and outgoing, displaying a discrete self-similarity reminiscent of that observed in critical collapse. Below the continuum threshold k_oo, and except at the discrete values k_n, the baryonic fluid drops through the Cauchy horizon, and in this case undergoes a shock, downstream of which the solution terminates at an irregular sonic point where the proper acceleration diverges, and there is no consistent self-similar continuation to zero radius. As far as the solution can be followed inside the Cauchy horizon, the radial direction is timelike. If the radial direction remains timelike to zero radius (which cannot be confirmed because the self-similar solutions terminate), then there is presumably a spacelike singularity at zero radius inside the Cauchy horizon, which is distinctly different from the vacuum (Reissner-Nordstrom) solution for a charged black hole.
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This paper presents a new 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.
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