Stability of gravitational and electromagnetic geons

Perry, G. P.; Cooperstock, F. I.

doi:10.1088/0264-9381/16/6/321

Cited by 33 publications

(42 citation statements)

References 21 publications

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“…While we are in agreement with him that it is indeed impossible with geons (but from a different line of reasoning, see [26], [27]), the argument is irrelevant because the galactic field is weak and hence geons are a priori out of the question, even if they were viable in principle.…”

Section: Replies To Various Analysessupporting

confidence: 62%

“…The novel aspect is that the lowest order equation (of order G 1/2 ) in (28) has zero on the RHS and the second equation that would normally be the Newtonian Poisson equation, differs in that it has non-linear terms. Thus, the structure of our solution does not proceed as in the standard approach of (27). In the latter standard approach, the lowest order base solution is the Newtonian solution whereas in the galactic problem, the lowest order equation is the Laplace equation for which an order G 1/2 solution is necessary (see [25] where this component is inappropriately chosen to be zero) and the next order (order G 1 ) equation for the density (29),…”

Section: Replies To Various Analysesmentioning

confidence: 99%

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Galactic Dynamics via General Relativity: A Compilation and New Developments

Cooperstock

Tieu

2007

Int. J. Mod. Phys. A

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We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite of the weak gravitational field and the non-relativistic source velocities, the mathematical system is still seen to be non-linear. It is shown that the rotation curves for various galaxies as examples are consistent with the mass density distributions of the visible matter within essentially flattened disks. This obviates the need for a massive halo of exotic dark matter. We determine that the mass density for the luminous threshold as tracked in the radial direction is 10 −21.75 kg·m −3 for these galaxies and conjecture that this will be the case for other galaxies yet to be analyzed. We present a velocity dispersion test to determine the extent, if of any significance, of matter that may lie beyond the visible/HI region. Various comments and criticisms from colleagues are addressed.

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Section: Replies To Various Analysessupporting

confidence: 62%

Section: Replies To Various Analysesmentioning

confidence: 99%

Galactic Dynamics via General Relativity: A Compilation and New Developments

Cooperstock

Tieu

2007

Int. J. Mod. Phys. A

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“…While we are in agreement with him that it is indeed impossible with geons (but from a different line of reasoning, see [107], [108]), the argument is irrelevant because the galactic field is weak and hence geons are a priori out of the question, even if they were viable in principle.…”

supporting

confidence: 62%

Back Matter

2009

General Relativistic Dynamics

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An issue first raised privately to us by some colleagues and later in [101], [102] concerns the nature of the matter distribution in our galactic model. They have noted that given the existence of the discontinuity of the function N z that we had pointed to in [63], a significant surface tensor S k i can be constructed with a surface density component given by to first order in G, i.e. G 1 . The square bracket notation [..] denotes the jump over a discontinuity of the given function, here at z = 0. Using (9.7), this becomesIt was claimed that this necessarily implied the existence of a singular physical surface of mass in the galactic plane above and beyond the continuous mass distribution that we had found, thus rendering our model unphysical.Having received this challenge, we calculated the surface mass that was said to be present in the four galaxies that we had studied by integrating (A.2) over the surface without paying heed to the actual sign of the result. Suspicions were aroused from the discovery that (A.2) in each case gave a numerical value slightly less than the mass that we had derived from the volume integral of our entire continuous mass density distribution using (9.18), (9.15) and (9.12). a With echoes from undergraduate mathematics courses, this pointed to a plausible explanation: in our case, with our choice of model, there is no physical mass layer present on the z = 0 plane. The surface integral of this singular layer is merely a mathematical construct that indirectly describes most of the continuously distributed mass by means of the Gauss divergence theorem. To see this, consider the vector F defined as bas a first option. We choose A(r, z) so thatwhere M is the total mass. As a more transparent second option, we choosewhere we definea It should be noted that the two terms in (A.2) were found to contribute equally.b er and ez are unit vectors in the r and z directions. A. CRITICAL CHALLENGES AND OUR REPLIES 197From these definitions, we deduce the form of A(r, z) in order to produce the density as expressed through N in (9.12). We calculate the mass over the cylindrical volume defined by −∞ < z < ∞, 0 < r < r galaxy . By the Gauss divergence theorem, the volume integral of ρ, via (A.7) is equal to the integral of the normal component of F over the bounding surfaces. However, the integration must be over a continuous domain and since the e z component is discontinuous over the z = 0 plane, the volume integral must be split into an upper and a lower half (see Figure A.1). The two new surface integrals together would constitute the jump integral of (A.2) in the first option if one were to be cavalier about the directions of unit outward normals, as we shall discuss in what follows. The surfaces above and below the galaxy give zero because of the exponential factors in z and the final small contribution comes from the cylinder wall via the A function. In our solution, the actual physical distribution of mass is not in concentrated layers over bounding surfaces: the Gauss theorem gives the va...

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“…If a vector having the length V initial has been transported round a closed loop, and arrived at the starting point, the new length according to (14) will be…”

Section: Parallel Displacement In Weyl's Geometrymentioning

confidence: 99%

Wesson’s Induced Matter Theory with a Weylian Bulk

Israelit

2005

Found Phys

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The foundations of Wesson's induced matter theory are analyzed. It is shown that the empty-without matter-5-dimensional bulk must be regarded as a Weylian space rather than as a Riemannian one. Revising the geometry of the bulk, we have assumed that a Weylian connection vector and a gauge function exist in addition to the metric tensor. The framework of a Weyl-Dirac version of Wesson's theory is elaborated and discussed. In the 4-dimensional hypersurface (brane), one obtains equations describing both fields, the gravitational and the electromagnetic. The result is a geometrically based unified theory of gravitation and electromagnetism with mass and current induced by the bulk. In special cases on obtains on the brane the equations of Einstein-Maxwell, or these of the original induced matter theory.

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Stability of gravitational and electromagnetic geons

Cited by 33 publications

References 21 publications

Galactic Dynamics via General Relativity: A Compilation and New Developments

Galactic Dynamics via General Relativity: A Compilation and New Developments

Back Matter

Wesson’s Induced Matter Theory with a Weylian Bulk

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