Can Maxwell's equations be obtained from the continuity equation?

We formulate an existence theorem that states that given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of four field equations. If the theorem is applied to the usual electromagnetic charge and current densities, the retarded fields are identified with the electric and magnetic fields and the associated field equations with Maxwell's equations. This application of the theorem suggests that charge conservation can be considered to be the fundamental assumption underlying Maxwell's equations.Comment: 14 pages. See the comment: "O. D. Jefimenko, Causal equations for electric and magnetic fields and Maxwell's equations: comment on a paper by Heras [Am. J. Phys. 76, 101 (2008)].

The general relativistic infinite plane

Uniform fields are one of the simplest and most pedagogically useful examples in introductory courses on electrostatics or Newtonian gravity. In general relativity there have been several proposals as to what constitutes a uniform field. In this article we examine two metrics that can be considered the general relativistic version of the infinite plane with finite mass per unit area. The first metric is the 4D version of the 5D "brane" world models which are the starting point for many current research papers. The second case is the cosmological domain wall metric. We examine to what extent these different metrics match or deviate from our Newtonian intuition about the gravitational field of an infinite plane. These solutions provide the beginning student in general relativity both computational practice and conceptual insight into Einstein's field equations. In addition they do this by introducing the student to material that is at the forefront of current research.Comment: Accepted for publication in the American Journal of Physic

Using the Uncharged Kerr Black Hole as a Gravitational Mirror

We extend the study of the possibility to use the Schwarzschild black hole as a gravitational mirror to the more general case of an uncharged Kerr black hole. We use the null geodesic equation in the equatorial plane to prove a theorem concerning the conditions the impact parameter has to satisfy if there shall exist boomerang photons. We derive an equation for these boomerang photons and an equation for the emission angle. Finally, the radial null geodesic equation is integrated numerically in order to illustrate boomerang photons.Comment: 11 pages Latex, 3 Postscript figures, uufiles to compres

Gravitational coupling to two-particle bound states and momentum conservation in deep inelastic scattering

The momentum conservation sum rule for deep inelastic scattering (DIS) from composite particles is investigated using the general theory of relativity. For two 1+1 dimensional examples, it shown that covariant theories automatically satisy the DIS momentum conservation sum rule provided the bound state is covariantilly normalized. Therefore, in these cases the two DIS sum rules for baryon conservation and momentum conservation are equivalent

Bohmian Quantum Gravity in the Linear Field Approximation

In this paper we have applied Bohmian quantum theory to the linear field approximation of gravity and present a self--consistent quantum gravity theory in the linear field approximation. The theory is then applied to some specific problems, the Newtonian limit, and the static spherically symmetric solution. Some observable effects of the theory are investigated

The equivalence principle, uniformly accelerated reference frames, and the uniform gravitational field

The relationship between uniformly accelerated reference frames in flat spacetime and the uniform gravitational field is examined in a relativistic context. It is shown that, contrary to previous statements in the pages of this journal, equivalence does not break down in this context. No restrictions to Newtonian approximations or small enclosures are necessary

Expansion-induced contribution to the precession of binary orbits

We point out the existence of new effects of global spacetime expansion on local binary systems. In addition to a possible change of orbital size, there is a contribution to the precession of elliptic orbits, to be added to the well-known general relativistic effect in static spacetimes, and the eccentricity can change. Our model calculations are done using geodesics in a McVittie metric, representing a localized system in an asymptotically Robertson-Walker spacetime; we give a few numerical estimates for that case, and indicate ways in which the model should be improved.Comment: revtex, 7 pages, no figures; revised for publication in Classical and Quantum Gravity, with minor changes in response to referees' comment

What is the topology of a Schwarzschild black hole?

We investigate the topology of Schwarzschild's black hole through the immersion of this space-time in spaces of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschild's black hole.Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1102.446

Formal analogies between gravitation and electrodynamics

We develop a theoretical framework that allows us to compare electromagnetism and gravitation in a fully covariant way. This new scenario does not rely on any kind of approximation nor associate objects with different operational meaning as it's sometime done in the literature. We construct the electromagnetic analogue to the Riemann and Weyl tensors and develop the equations of motion for these objects. In particular, we are able to identify precisely how and in what conditions gravity can be mapped to electrodynamics. As a consequence, many of the gemometrical tools of General Relativity can be applied to Electromagnetism and vice-versa. We hope our results would shed new light in the nature of electromagnetic and gravitational theories.Comment: 9pages, submitted to General Relativity and Gravitatio

A Deeper Look at Student Learning of Quantum Mechanics: the Case of Tunneling

We report on a large-scale study of student learning of quantum tunneling in 4 traditional and 4 transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research, students still struggle with many of the same issues found in other courses. However, the reasons for these difficulties are more subtle, and many new issues are brought to the surface. By explicitly addressing how to build models of wave functions and energy and how to relate these models to real physical systems, we have opened up a floodgate of deep and difficult questions as students struggle to make sense of these models. We conclude that the difficulties found in previous research are the tip of the iceberg, and the real issue at the heart of student difficulties in learning quantum tunneling is the struggle to build the complex models that are implicit in experts' understanding but often not explicitly addressed in instruction.Comment: v2, v3 updated with more detailed analysis of data and discussion; submitted to Phys. Rev. ST: PE