decraig

Do you expect a different result by changing coordinate systems?

Correct. The event horizon is a multiplicity of coordinate singularites. Do you have anything substantial to contribute? I have 30 years in topics of mathematical physics. You need to do better than picking nits.

electrons are tiny little point like particles that collide with other little point like particles giving off point-like particles called photons. Since this is the usual point of view we should never point out that the probability that a finite number of moving points colliding with other points on a 3D manifold is zero.

As I understand it, the continued acceleration due to dark energy results in a metric with ever larger components of tension. At some point the tension should be in the order of magnitude of the strong force holding the quarks of both bosons and mesons together. How would the physical situation appear?

Do I have this right? A completely antisymmetric tensor or type (0,k) on a k dimensional manifold in orthonormal coordinates may be expressed as a scalar times the Levi-Civita symbol, [math]\epsilon_{\mu \nu \rho \sigma}[/math]. Under a general linear transformation, is the result also a scalar times the Levi-Civita symbol?

1) Gravity prevents further collapse without the need of pressures due to matter. I've addressed this way back and multiple times. I guess you're irritated because I haven't directly answered your posts. Understandable. Completely wrong. My dislike of black holes reflects my dislike of pseudo science. Perhaps you might examine your own objectivity if you have the skills in physics, or the manner in which you defer to authority if you don't. So what do you have as best evidence that I already haven't shot down? Post any website or article written in English. ---------------------------------------------------------------------------------------- If anyone really wants to contribute, they should link professionally written supporting articles, rather than hearsay, gossip, or pop-physics lacking substantial support. A derivation of the distance to event horizon or the central singularity for the general solution would be nice. If you really want to pursue possibly viable arguments arguments against my stance, you might find something on naked singularities, an argument on physically measurable differences between black holes and incipients, or something in string theory.

The purpose of this thread was to find experimental and theoretical support for black holes. There are other threads about black holes where existence is not questioned. Physical Evidence: So far, I have found no supporting arguments or references to arguments of support. General Relativity: Inwardly falling uncharged matter, having zero angular momentum does not obtain a Schwarzschild solution before hell freezes over using general relativity without quantum mechanical considerations. It would seem the general solution would be the same. Quantum Mechanics: Any hypothetical quantum solution would require violation of local causality--information would have to be transmitted at greater than the speed of light. Such a solution would admit 'time travel'; there would exist an inertial frame where matter would be in both the interior and the exterior at the same time. Sounds like Star Trek to me. No one has addressed this issue nor presented reference articles in argument. Psychology: The desire for belief in these objects has attracted a following of religious quality. This social phenomena is currently played-out on the science channel, where the announcer declares their existence to be indisputable fact.

Wikipedia has both a defintion and a list of 6 items. 1) Force amplification of a hydraulic system meets the definition but is not on the list. Neither are electrical amplification, an airfoil, nor a 1953 pontiac hydromatic transmission clutch. Apparently pulley ropes are floppy, but OK, but other non-rigid elements are not. Seems arbitrary. 2) At one time, some people were attempting to lobby their novel 7th simple machine for inclusion. It consisted of two cylinders in a rectangular frame with an S shaped band of flexible material threaded between the cylinders

No, I mean doable as in solvable. If the assigned charges in your measuring instrument also changed sign, there would be no measurable effect. But I see what you mean. For a local parity change on a system, where the observer is outside a region of coordinate invertion--which is what you are talking about--there would be a measurabe difference. But what of a global change?

This, however, should still be do-able in the usual calculus, Studiot

In short, charge would change sign upon conjugating any spatial coordinate. e.g.: [math]C(x^i)=-x^i[/math] In the usual div-grad-curl calculus used, the declaration doesn't derive from anywhere--its just declared. But we can do a little better, as follows. In preliminarty justification, total charge, Q is the integral over a space-like region of charge density, q = q(x,y,z). [math]Q= \int _s q[/math]. q is the charge density, a type (0,3) tensor. It may appear as if the integrating infinitesimals are missing. They are not; but are the tensor bases. If the volume element is oriented we could define charge density as q = q_{xyz} dxdydz where q is antisymmetric in all indices. The sign of Q follows the sign of q.

I haven't found a good answer to this. Deferring to charge accelerating in an antenna ignores all higher order terms. The axial symmetric Larmor model seems to lead to energy conservation problems for a free particle. Maybe I'm mistaken. What pattern of electromagnetic radiation results? The magnitude of the on-axis radiation is zero. Also, (1/2)(E^2+B^2) values are equal on each side of the yz-plane for charged particles traveling in the x direction, within a co-axial static electric field. This implies the kinetic energy of charges is not reduced by any radiation. This implies the static electric field is the source of radiated electromagnetic energy. But the electrostatic field remains unchanged after the particle has passed between the plates. This implies energy is not properly conserved.

No, not the E-B vacuum duality, though interesting in itself and may be extended using complex charge. It's the same as the F-G duality, where F is the Farday tensor and G its Hodge dual. It's extended using F+iG --> *(iF-G), and **(iF-G)--> -F-iG, if I recall. * is the Hodge duality operator. The magnetic charge can removed with a global gauge change. I'm asking about PT symmetry in Maxwell + Lorentz force.

In the normal description, E, J and the vector potential A are taken to be vectors. B is an axial vector. q is a scalar. Would any physical description change should these roles be reversed? For example, B would become a vector, E would become an axial vector, and q a pseudo scalar.

I didn't imply non-existence. No, one of the first things to do is compare the time it takes things to transpire.

The mass of light confined to a cavity is non-zero. It happens to be double the expected value. The discrepancy is made-up by the tension induced by light pressure to the confining structure. How big are your little electrons?

The rate of discharge is limited by the battery's own internal impedance.

Spaghettification seems to be another misunderstanding of black hole physics. Perhaps someone could quote Hawking in "A Brief History of Time" to see exactly how this became a common belief. For a large enough object the tidal forces are weak enough that an object does not tear itself apart outside the event horizon. In current understanding of cosmology tensile forces due to dark energy would win the race, and take apart the atoms of which an object is made, before this would occur.

The quanta of electromagnetism: The inertial mass is independent of minkowski coordinate system. It combines in superposition; it is spin 1. Its intrinsic mass is rational in any system of measurement. The phase velocity and group velocity of a free particle are equal independent of the direction of measurement. The photon is it's own antiparticle. Its baryon number is zero. Its isospin is zero. It has no other family members; it does not exist as a resonance of multiple family members. It is colorless. It's electric and magnetic charge are zero. It has multiple classical gauge invariances-- 3 or 4 I think. It has zero dipole moment. What other particle is this featureless? Note that photons have more than just properties of energy. See particle properties here http://en.wikipedia.org/wiki/List_of_particles So they are not just "pure energy"--whatever that could mean. 2nd: "Energy" is a highly overrated physical quantity. It is not conserved--even in Newtonian physics. 3rd: You speak of "a photon". What photon? As particles they are indistinguishable, and even how many photons are existent in a system is an uncertainty.

All of the particulars of this can be found in Sean Carrol's http://preposterousuniverse.com/grnotes/ chapter 3. Of course this means doing all the hard work in chapters 1 through 3, but some will find it well worth it. There is no better author for a conversational approach to a topic that could be otherwise be very dry. There is more than one way to define a geodesic on the manifold of spacetime, and more than one shortest-distance definition. All the complication arises in the ambiguity of choosing the definition of the derivative of a vector, and other objects where the manifold is not Minkowskian--that is, not flat. The definition of a geodesic in general relativity reduces to the path of an unaccelerated particle where the spacetime manifold is sufficiently flat. This involves about 6 separate requirements to say how the derivatives themselves are to be distinguished from all other possible definitions.

The energy, W can be expressed in two parts. From the electric field alone, the energy density [math]w_f = (1/2) \epsilon E^2[/math]. This is from the electromagnetic stress-energy tensor. This has to be integrated, or added-up over the volume. [math] \epsilon[/math] is the permittivity of the dielectric. From the Lorentz force for the electric field, [math]W_p= \int^{d} F dx = dEq[/math]. q is the charge on one plate. d is the plate separation. For other than a vacuum, we would have to include the charge displacement within the dielectric. This is via use of the microscopic Maxwell equations were there is no displacement current term, D.

I don't know how to break-up a quote so I will refer to your comments by paragraph. Par.1: They don't. Par.2: I did not read-in this presupposition. In fact, they are aware that GR alone does not lead to an event horizon but would require something more than quantum tunneling. I did the math for a spherically symmetrical non-solution in post #29. Par. 3: Penrose and Hawking gloss over formation, and continue forth as if it were established fact, or perhaps left it for others. This is what seems to have lead to general popular confusion and false claims. I don't know what "bugus" means. The horizon would be what is called a "coordinate singularity where the metric tensor is not well defined." The designation 'coordinate' means that there exists at least one coordinate basis where the metric is well defined. This is unlike the central singularity which is not well defined in any coordinate system. If you want to see what this looks like go the the wiki for the Schwarztchild solution and set R_s=R. Par. 4. No. The models are static solutions. Formation, using gr alone, would require a non-static solution.

I've been looking for a generally covariant representation of the 4-velocity as a k-form of the velocity, that when self-integrated over k dimensions results in a velocity valued pseudo scalar that is, at the least, Lorentz invariant. This would be a velocity analog of the 3-form charge-current density.

I don't know what to tell you. I've been over, and over this material. I posted these articles on the current state of research, that I know of. If you know of others, I would be pleased to know. But how these researchers 'feel' their research should evolve doesn't argue well with me. Where have I thrown away the mathematical formalism of GR?? I know of no supportive observational evidence that can distinguish a black hole from an incipient black hole. Do you have supportive documents?

The following lists some most recent articles as submitted to the arXivs concerning the formation of black holes. First, there is a central issue to be addressed here. It is a common misunderstanding and drives the objections to my speculations. General relativity is not Newtonian gravity. 1) Gravity hinders or inhibits or prevents the formation of black holes. Specifically this is the time-time term of the stress-energy tensor (See the Wiki). Welcome to the 21st century. 2) What mighty allow formation of an event horizon? Jumping energy over a boundary in finite time per an external observer. The issue is unresolved, with contradictory conclusions among researchers probing vairous applications of quantum mechanics. To the best of my knowledge the current state of affairs concerning black hole formation, and therefore existence, is subsumed in the following: "A clear advantage of the present approach is that the action for the system greatly simplifies in the interesting limit of an incipient black hole and raises the hope that a solution, even to the notorious back-reaction problem, may be within reach." This is a quote from my second reference, below. What did this say? Nobody knows boy and girls. Nobody knows if there is a physical mechanism of formation. As I said above, these are objects of extraordinary claim. And possess heuristic problems as well. (I claim hypervalent Iodine that Steven Hawking and Suskin are arguing over the shade of invisible pink polka-dot unicorns Steven says are hiding in his basement. See the following references. You claim "...since black holes are an accepted model in physics..." This lazy nature may be good enough for cosmologists and those who do not research black holes, but is not at all evident among those that actually do.) arXiv:1307.5861 [pdf, ps, other] Icezones instead of firewalls: extended entanglement beyond the event horizon and unitary evaporation of a black hole John Hutchinson, Dejan Stojkovic Comments: 10 pages, 4 figures. v2: construction of icezone density matrix, 12 pages Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc) 2013 arXiv:0711.0006 [pdf, ps, other] Schrodinger Picture of Quantum Gravitational Collapse Tanmay Vachaspati Comments: 9 pages, 1 figure. Matches published version Journal-ref: Class.Quant.Grav.26:215007,2009 Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th) arXiv:gr-qc/0701096 [pdf, ps, other] Quantum Radiation from Quantum Gravitational Collapse Tanmay Vachaspati, Dejan Stojkovic Comments: accepted for publication in Phys. Lett. B Journal-ref: Phys.Lett.B663:107-110,2008 Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th) arXiv:0806.0628 [pdf, ps, other] Hawking radiation as seen by an infalling observer Eric Greenwood, Dejan Stojkovic Comments: Added analysis of the Hawking-like radiation as seen by an observer in Eddington-Finkelstein coordinates. Accepted for publication in JHEP Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th) 2008 arXiv:gr-qc/0609024 [pdf, ps, other] Observation of Incipient Black Holes and the Information Loss Problem Tanmay Vachaspati, Dejan Stojkovic, Lawrence M. Krauss Comments: 15 pages; 9 figures. Changes made in response to referee's comments and to clarify arguments, in particular to describe clearly that the results represent observations made by an asymptotic observer. Accepted for publication in Phys. Rev. D Journal-ref: Phys.Rev.D76:024005,2007 Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th) arXiv:hep-ph/0505026 [pdf, ps, other] Holes in the walls: primordial black holes as a solution to the cosmological domain wall problem Dejan Stojkovic, Katherine Freese, Glenn D. Starkman Comments: References added; Published in Phys. Rev. D Journal-ref: Phys.Rev. D72 (2005) 045012 Subjects: High Energy Physics - Phenomenology (hep-ph); Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc) arXiv:gr-qc/0604072 [pdf, ps, other] Information-preserving black holes still do not preserve baryon number and other effective global quantum numbers Dejan Stojkovic, Glen D. Starkman, Fred C. Adams Comments: Honorable Mention on Gravity Essay Competition 2005; Published in the special Essay issue of Int.J.Mod.Phys Journal-ref: Int.J.Mod.Phys. D14 (2005) 2293-2300 Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th)