Physics

The density profiles of dark matter halos are often modeled by an approximate solution to the isothermal Lane-Emden equation with suitable boundary conditions at the origin. It is shown here that such a model corresponds to an exact solution of the Einstein-Maxwell equations for exotic charged dust. It is also shown that, because of its necessarily very small charge to mass ratio, the fact that the particles are charged does not necessarily rule out such material as a candidate for dark matter.

Dark Matter-Charged Exotic Dust

Version published in Journal of Physics and Astronomy, Volume 2, Issue 3 (2013):

J Phys & Astron-Chrged Exotic Dust

Plane electromagnetic and gravitational waves interact with particles in such a way as to cause them to oscillate not only in the transverse direction but also along the direction of propagation. The electromagnetic case is usually shown by use of the Hamilton-Jacobi equation and the gravitational by a transformation to a local inertial frame. Here, the covariant Lorentz force equation and the second order equation of geodesic deviation followed by the introduction of a local inertial frame are respectively used. It is often said that there is an analogy between the motion of charged particles in the field of an electromagnetic wave and the motion of test particles in the field of a gravitational wave. This analogy is examined and found to be rather limited. It is also shown that a simple special relativistic relation leads to an integral of the motion, characteristic of plane waves, that is satisfied in both cases.

Canadian Journal of Physics 89, 1187-1194 (2011).

Electromagnetic and Gravitational Waves: The Third Dimension

Foundations of Physics Vol. 38, pp. 959-968 (2008)

The original publication is available at www.springerlink.com

http://dx.doi.org/10.1007/s10701-008-9245-x

It has been shown that for the Reissner-Nordstrom solution to the vacuum Einstein field equations charge, like mass, has a unique space-time signature [Found. Phys. 38, 293-300 (2008)]. The presence of charge results in a negative curvature. This work, which includes a discussion of effective mass, is extended here to the Kerr-Newman solution.

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The assumption that the vacuum is the minimum energy state, invariant under unitary transformations, is fundamental to quantum field theory. However, the assertion that the conservation of charge implies that the equal time commutator of the charge density and its time derivative vanish for two spatially separated points is inconsistent with the requirement that the vacuum be the lowest energy state. Yet, for quantum field theory to be gauge invariant, this commutator must vanish. This essay explores how this conundrum is resolved in quantum electrodynamics.
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It will be argued here that the cosmological constant problem exists because of the way the vacuum is defined in quantum field theory. It has been known for some time that for QFT to be gauge invariant certain terms—such as part of the vacuum polarization tensor must be eliminated either explicitly or by some form of regularization followed by renormalization. It has recently been shown that lack of gauge invariance is a result of the way the vacuum is defined, and redefining the vacuum so that the theory is gauge invariant may also offer a solution to the cosmological constant problem.

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Foundations of Physics Vol. 38, pp. 293-300 (2008).

The original publication is available at www.springerlink.com

http://dx.doi.org/10.1007/s10701-008-9209-1

Charge, like mass in Newtonian mechanics, is an irreducible element of electromagnetic theory that must be introduced ab initio. Its origin is not properly a part of the theory. Fields are then defined in terms of forces on either masses–in the case of Newtonian mechanics, or charges in the case of electromagnetism. General Relativity changed our way of thinking about the gravitational field by replacing the concept of a force field with the curvature of space-time. Mass, however, remained an irreducible element. It is shown here that the Reissner-Nordstrom solution to the Einstein field equations tells us that charge, like mass, has a unique space-time signature.

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In contrast to the Schwarzschild solution, the infinite red shift surfaces and null surfaces of the Kerr solution to the axially-symmetric Einstein field equations are distinct. Some unusual infinite red shift surfaces for observers following the time-like Killing vector are displayed here for the Kerr and Kerr-Newman solution. Some similarities of the latter to the Reissner-Nordstrom solution are also discussed.

(arXiv: gr-qc/0702114)

Journal of Physics & Astronomy Vol. 2, Issue 4.

JOPA_InfRedShiftSurf