Classical Electrodynamics in Quasi-Metric Space-Time

Details Classical Electrodynamics in Quasi-Metric Space-Time Classical Electrodynamics in Quasi-Metric Space-Time

2003-03-26

arxiv.org/abs/gr-qc/0303107v5

Grav.Cosmol. 12 (2006) 262-272

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, v2: major revision; v3: errors corrected, exact solution found; v4: accepted for publication in G&C; v5: minor corre

Scientific paper

In quasi-metric relativity it is necessary to separate between 2 different versions of the electromagnetic field tensor (EMFT): (1) The active EMFT determining the electromagnetic contribution to the active stress-energy tensor, and (2) The passive EMFT entering the equations of motion. The passive EMFT may be found from the usual Maxwell's equations in curved space-time, and local conservation laws for passive electromagnetism ensure that photons move on null geodesics in quasi-metric space-time. However, by construction the norm of the passive EMFT decreases secularly, defining a global cosmic attenuation (not noticeable locally) of the electromagnetic field. As a simple example the gravitational and electric fields outside a spherically symmetric, metrically static, charged source are calculated. It is found that the global cosmic expansion affects the electric and the gravitational fields differently, i.e., unlike the gravitational field the electric field does not expand. On the other hand, if radiative effects can be neglected it is found that electromagnetically bound, classical systems will participate in the cosmic expansion. But since quantum-mechanical states should not be affected by the expansion, there is no reason to believe that this calculation should apply to quantum-mechanical systems such as atoms. Finally it is shown that the main results of geometric optics hold in quasi-metric space-time.

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