1,721,032 research outputs found
An explicit representation for the axisymmetric solutions of the free Maxwell equations
Full text link16 pages. V3: abstract simplified, introduction and conclusion reinforced, Eqs. (18)-(20) addedGaray-Avendano & Zamboni-Rached (2014) defined two classes of axisymmetric solutions of the free Maxwell equations. We show that, by combining these two classes of solutions, one is able to describe in explicit form all time-harmonic axisymmetric free Maxwell fields, and hence, by summation on frequencies, all axisymmetric free Maxwell fields. This provides an explicit representation for these fields. It will be important, e.g., to have the interstellar radiation field in a disc galaxy modelled as an exact solution of the free Maxwell equations
Space isotropy and weak equivalence principle in a scalar theory of gravity
No full text24 pages. Published version is Open Access at http://www.sbfisica.org.br/bjp/files/v36_177.pdfWe consider a preferred-frame bimetric theory in which the scalar gravitational field both influences the metric and has direct dynamical effects. A modified version ("v2") is built, by assuming now a locally-isotropic dilation of physically measured distances, as compared with distances evaluated with the Euclidean space metric. The dynamical equations stay unchanged: they are based on a consistent formulation of Newton's second law in a curved space-time. To obtain a local conservation equation for energy with the new metric, the equation for the scalar field is modified: now its l.h.s. is the flat wave operator. Fluid dynamics is formulated and the asymptotic scheme of post-Newtonian approximation is adapted to v2. The latter also explains the gravitational effects on light rays, as did the former version (v1). The violation of the weak equivalence principle found for gravitationally-active bodies at the point-particle limit, which discarded v1, is proved to not exist in v2. Thus that violation was indeed due to the anisotropy of the space metric assumed in v1
On the equations of electrodynamics in a flat or a curved spacetime and a possible interaction energy
No full text25 pages. V3: Small precisions added (end of 1st paragraph on p. 2, bottom of p. 23): as appeared in Open Physics except for slight language editing.International audienceWe investigate which are the independent equations of continuum electrodynamics and what is their number, beginning with the standard equations used in special and in general relativity. We check by using differential identities that there are as much independent equations as there are unknowns, for the case with given sources as well as for the general case where the motion of the charged medium producing the field is unknown. Then we study that problem in an alternative theory of gravity with a preferred reference frame, in order to constrain an additional, "interaction" energy tensor that has to be postulated in this theory, and that would be present also outside usual matter. In order that the interaction tensor be Lorentz-invariant in special relativity, it has to depend only on a scalar field p. Since the system of electrodynamics of the theory is closed in the absence of the interaction tensor, just one scalar equation more is needed to close it again in the presence of p. We add the equation for charge conservation. We derive equations that will allow one to determine the field p in a given weak gravitational field and in a given electromagnetic field
Progress in evaluating a possible electromagnetic interaction energy in a gravitational field
No full text13 pages. Text of a talk given at the 14th Conf. on Classical and Quantum Relativistic Dynamics of Particles and Fields (IARD 2024: Helsinki, June 3-6, 2024). N.B.: the published version has 7 references less: some quotations of previous work by the author replaced by "see Ref. [N] and references therein".International audienceThe Lorentz-Poincaré interpretation of special relativity (SR) keeps the classical concepts of separated space and time, at the price of postulating an indetectable preferred inertial frame or "ether". But SR does not contain gravity. The presence of gravity could make the ether detectable. This is one idea behind the "scalar ether theory of gravitation" (SET), which coincides with SR if the gravity field vanishes, and passes a number of tests. However, the coupling of SET with the Maxwell electromagnetic (EM) field needs to use the theory's dynamical equation for the energy tensor in a non-trivial way. It cannot be assumed that the energy tensors of the charged matter and the EM field add to give the total energy tensor,source of the gravitational field. Thus, an additional, "interaction" energy tensor T_inter has to be postulated. Asking that T_inter is Lorentz-invariant in the situation of SR, fixes its form. It depends only on a scalar field p. T_inter is an exotic kind of matter and is distributed in the whole space, hence it could contribute to dark matter. For a weak gravitational field, p obeys a first-order partial differential equation (PDE) involving the EM field and the Newtonian potential. However, the EM field varies on the scale of the wavelength, which is extremely small. To get the field p in a galaxy, some averaging has to be done. After several attempts based on the homogenization theory, a simpler way has been found recently: If the macro-averages of p and the EM field vary smoothly, it can be shown that the PDE for p remains valid in the same form with spacetime-averaged fields. The current stage of calculations will also been shown
Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation
Full text link33 pages. V5: version appeared in Open Physics (Open Access, see DOI): still a few redactional improvements so that the paper read more smoothly.International audienceAn alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton's second law. This implies Einstein's geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell's equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a ``free" photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field
The Scalar Ether-Theory of Gravitation and its First Test in Celestial Mechanics
No full textLaTeX, 6 pages, one figure. Text of a talk at the 5th Friedmann International Seminar on Gravitation and Cosmology, Joao Pessoa (Brazil), 23-30 April 2002.The motivations for investigating a theory of gravitation based on a concept of ëther\" are discussed-- a crucial point is the existence of an alternative interpretation of special relativity, named the Lorentz-Poincar\\é ether theory. The basic equations of one such theory of gravity, based on just one scalar field, are presented. To check this theory in celestial mechanics, an äsymptotic\" scheme of post-Newtonian (PN) approximation is summarized and its difference with the standard PN scheme is emphasized. The derivation of PN equations of motion for the mass centers, based on the asymptotic scheme, is outlined. They are implemented for the major bodies of the solar system and the prediction for Mercury is compared with an ephemeris based on general relativity
Is spacetime as physical as is space?
No full text25 pages. V3: Introduction largely expanded to detail the origin of the concepts. A few wording improvements in the body of the paper. Fourteen more references. Appeared in the Journal of Geometry and Symmetry in Physics, Vol. 46, pp. 1-24 (2017)International audienceTwo questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a congruence of reference trajectories, defines a physical space. The points of that space are formally defined to be the world lines of the congruence. That space can be endowed with a natural structure of 3-D differentiable manifold, thus giving rise to a simple notion of spatial tensor --- namely, a tensor on the space manifold. The second question is: does the geometric structure of the spacetime determine the physics, in particular, does it determine its relativistic or preferred-frame character? We find that it does not, for different physics (either relativistic or not) may be defined on the same spacetime structure --- and also, the same physics can be implemented on different spacetime structures
Interstellar radiation as a Maxwell field: Improved numerical scheme and application to the spectral energy density
No full textThe existing models of the interstellar radiation field (ISRF) do not produce a Maxwell field. Here, the recent model of the ISRF as a Maxwell field is improved by considering separately the different frequencies at the stage of the fitting. Using this improved procedure: (i) It is checked in detail that the model does predict extremely high values of the spectral energy density (SED) on the axis of a galaxy, which however decreases very rapidly when ρ\rho , the distance to the axis, is increased from zero. (ii) The difference between the SED values (with ρ=1\rho =1 or 8kpc8\hspace{0.33em}{\rm{kpc}}), as predicted either by this model or by a recent radiation transfer model, is reduced significantly. (iii) The slower decrease of the SED with increasing altitude zz, as compared with the radiation transfer model, is confirmed. We also calculate the evolutions of the SED at large ρ\rho . We interpret these evolutions by determining asymptotic expansions of the SED at large zz, and also ones at large ρ\rho
Charge conservation in a gravitational field in the scalar ether theory
No full text30 pages. V3: One minor misprint corrected before Eq (50), three short precisions added. Conforms exactly with the version to appear in Open Physics.International audienceA modification of the Maxwell equations due to the presence of a gravitational field was formerly proposed for a scalar theory with a preferred reference frame. With this modification, the electric charge is not conserved. The aim of the present work was to numerically assess the amount of charge production or destruction. We propose an asymptotic scheme for the electromagnetic field in a weak and slowly varying gravitational field. This scheme is valid independently of the theory and the " gravitationally-modified " Maxwell equations. Then we apply this scheme to plane waves and to a group of Hertzian dipoles in the scalar ether theory. The predicted amounts of charge production/destruction discard the formerly proposed gravitationally-modified Maxwell equations. The theoretical reason for that is the assumption that the total energy tensor is the sum of the energy tensor of the medium producing the electromagnetic (e.m.) field and the e.m. energy tensor. This means that an additional, " interaction " tensor has to be present. With this assumption, the standard Maxwell equations in a curved spacetime, which predict charge conservation, are compatible with the investigated theory. We find that the interaction energy might contribute to the dark matter
Gravity as Archimedes\' thrust and a bifurcation in that theory
Full text link24 pages, invited contribution to the Franco Selleri Festschrift. v3: Endnote 45 on absolute simultaneity improved (formerly footnote 6: class file changed to revtex4), a few references updated (and now with titles). v2: minor correction in subsect. 3.2, some wording improvements, and a few references addedEuler\'s interpretation of Newton\'s gravity (NG) as Archimedes\' thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Euler\'s, is recalled and compared with the latter. None of these two \"gravitational ethers\" can obey classical mechanics. This is logical since the ether defines the very reference frame, in which mechanics is defined. This concept is used to build a scalar theory of gravity: NG corresponds to an incompressible ether, a compressible ether leads to gravitational waves. In the Lorentz-Poincar\\é version, special relativity is compatible with the ether, but, with the heterogeneous ether of gravity, it applies only locally. A correspondence between metrical effects of uniform motion and gravitation is assumed, yet in two possible versions (one is new). Dynamics is based on a (non-trivial) extension of Newton\'s second law. The observational status for the theory with the older version of the correspondence is summarized
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