decraig

Just 2 days ago, Jan 8, 2016, the long awaited follow up paper arrived. http://arxiv.org/abs/1601.00921 Hawking, et al, describe a different sort of animal, not a black hole at all, in the sense that a black hole is defined as a region of space from which nothing can escape, not even light. I suggest naming this new object a "Foo' Hole." In case it has escaped notice, Foo' Holes and Black Holes are mutually exclusive theoretical objects. Should Hawking argue his theory on this site will he also be suspended, as I, by a moderator operating far outside his pay grade? Later. Much, much later.

You certainly do have a lot of questions. Can you explain your obsession with taking votes?

I believe you refer to the radial coordinate. But now I don't know what kind of solution to the field equations you might be talking about. Assuming spherical symmetry you want something like this: [math]c^2d \tau ^2 = f(r,t)c^2dt^2 - g(r,t)dx^2 - d \Omega ^2 [/math] What does that look like? It seems to violate Birkhoff's theorem... http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity)

Identify the principle, please.

If the metric changes with time, it is not the Schwarzschild metric. It would be a different metric. This is the Schwarzschild metric: Notice there are no terms containing 't' in the metric coefficients. A metric coefficient is the stuff in each term standing in front of ct^2, dr^2, dtheta^2 and dphi^2. You seem to have misunderstood. However, it is true that asymmetrical, irrotational matter will approach spherical symmetry under mutual gravitational attraction. This is due to gravitational time dilation where ingoing velocities of particles slow according to an external observer as they approach the Schwarzschild radius. This was demonstrated by Rodger Penrose. Penrose, Gravitational Collapse and Space-Time Singularities Physical Review Letters Vol. 14-3 1965 Penrose examines the dynamics of matter external to the Schwarzschild radius. He does not examine the dynamics of formation. Your words, “to form a symmetrical black hole,” seem to be something extra you added in expectation. Penrose continues with the post formation dynamics, ignoring the critical formation dynamics. No one in 1965 had a formation solution. They skipped it. They made a lot of progress explaining what things look like afterwards, but couldn’t find a way to get there. By all evidence this state of affairs persists today. Not properly understood, it is a source of militant denial. It ranges from accusations that I am wearing blinkers, accusing me of not conducting research--and by others, deliberate fraud.

I already explained what's wrong with your referencing. You're doing the same thing as the other guy. You're referenced an article. You did not cite any of its content. Did you get beyond the title? Should you have bothered to read it, you would know that the article addresses experimental evidence that would distinguish between dark clusters and black holes, but not highly condensed matter and black holes. Strange has something better to offer. Of course; there is a distinction. Consider you already have a spherical black hole of mass M, and we throw a small mass, m at it. Does m cross the event horizon? The mass, m perturbs our spherical black hole solution; the exact solution is not spherically symmetric. So we use some numerical method. By experience we know it's not exact either, and subject to modeling approximation and floating point round-off. But the error introduced may itself be analytical or subject to numerical analysis. I write a program to solve the n-body problem of multiple masses under mutual gravitational attraction. Each mass follows some curved path that I approximate with very small straight line section. To test the model I use a large central mass, and a small mass in circular orbit. Over time the orbital radius increased. I erroneously conclude that gravitational energy is not constant over time. dE/dt is greater than or equal to zero. This is a lot different than dE/dt=0. Making the straight line segments smaller does not change to result. Replacing the straight lines with polynomial approximational results in dE/dt=~0. For black holes, the region of interest is near Rs. The functions of interest are gtt( r ) = 1/(1- r/Rs) and grr( r ) =1- r/Rs where r is very close in magnitude to Rs. r-Rs=epsilon, epsilon-->0. Our numerical error will never be less than epsilon but we might try a change of coordinates, u=u(gtt,grr) and v=v(gtt,grr). We can then try doing the numerology in u and v than translate the results back to gtt and grr and hope that calculating gtt doesn't give us an NAN or stack overflow.

I have, many times already. And I just keep on getting false information, red herrings consisting of either irrelevant information of references that even contradict the claim made of them. Look for yourself. As to your second remark that I have put in bold, this is far from correct. Please show me an example where I have done this. Produce this information that is "actually out there". This was the intent of this thread, and no one have yet manged to produced it, yet insist that it is there. If unsupported claims are the stock in trade in this forum, why call it a science forum. I have enumerated approximately 6 points, unverifed that could falsify a conjecture of non-formation of black holes. I haven't seen any of these points raised. Notice that the Schwarzschild metric is invariant with time (it doesn't change over time). This metric solution is insufficient evidence of physical black holes formatationbecause to make one, the metric has to change with time. It looks good on paper and the drawings are attractive, but the map is not the territory. Do you see that you have to have a means of formation before you can justify models of existent black holes, or alternatively supply experimental evidence? I've already addressed this. I agree. You should not provide a consensus--provide evidence or scholarly papers instead. The ideal of science appeals to evidence not authority. As to your reference I have put in bold: Have you read the article. Can you cite the section where they provide distinguish evidence between BHs and highly collapsed matter? Is it even addressed? Evidence is evidence, but distinguishing evidence is what is require here. I'm glade you know GR quite well. All coordinate charts are nonlocal frames at points over their domain. By putting quotes around 'seems' are you implying that coordinate charts should not be used describe physics? Interesting. Do think that all charts with singular points are nonphysical?

pure nonsense

Without the moon, life on earth would be no more complex than bacterium applying accepted theory; the moon reduces the excursion of obliquity (axial tilt). Without the moon the axial tilt could vary as much as 80 degrees. With the moon the obliquity varies from about 22 to 24 degrees over a period of 40K years. However, there is some disagreement. http://io9.com/5829438/earth-doesnt-need-the-moon

Based upon these confused remarks, I don't think physics is your calling. You are not positively contributing to this thread but just trying to win an argument without supplying merit. This repeated invokation of Eddington-Finkelstein coordinates is immaterial. Per canon, mapping to EF coordinates does not affect physical results. The coordinate map between the Schwarzschild and EF charts is invertible over the coordinates range involved. Look it up. EF yields the same time for black hole formation as S. This is introductory level general relativity. If you are versed in elementary general relativity you will be able to name the canon to which I referred. This is a challenge to your credibility.

"My science teacher vaguely defined [energy] as the ability to do work." I don't think this is a very good definition, and says "energy is the ability to do energy". Formally, work has units of energy. In terms of forces, W = Fd. Work is force applied over a distance. It would be better so say that energy has at least two forms, kinetic and potential, and that one form can be become another. --------------------------------------------------- On energy conservation: 1) The energy of a system is not conserved. Energy can enter or escape the system. Rather, we might formulate what is called a 'continuity equation'. The change in energy of a system plus the momentum flux out of the system is constant. To keep it simple, envision a tesseract. The bottom face of the tesseract is the system at some time t_0. The top face is the system at some future time t_1. At t_0 the system has some initial energy. At some future time, t_1, the system will have another amount of energy. Now look at the remaining 6 faces. A 'face' on a tesseract is a cube. These 6 remaining cubes have two sides with units of length. The remaining side is an interval of time. The difference in energy of the top and bottom faces plus the differences in momentum of the remaining opposing faces is zero. This is a continuity equation. 2) An observer undergoing a change in velocity will find the energy of a system is not conserved; energy is not conserved under a general Galilean transformation; a change in velocity. This is because the kinetic energy has changed.

Doh! Yes, replacing c with bc is the obvious part I missed, such that, if b canels on both sides of a set of equations, then those equations are invariant under rescaling of c.

Thanks, for that. Add electric charge and you get the Reissner-Nordstrom metric, http://en.wikipedia.org/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric, with two critical radii. Reissner–Nordström

http://en.wikipedia.org/wiki/Smart_bullet#Changing_trajectory

The title should have been: "Is physics invariant under global regauging of c?" The geometrical constant relating dimensions of time and distance is c=~300,000 km/sec. Are the laws of physics invariant under regauging of c; that is [math]c \leftarrow c' = b c[/math] where b is real scalar? I'm sure there's something obvious I'm missing.