In the first half of this thesis a local electrodynamics ofmedia in given non-inertial frames*, within Maxwell-Einstein classicalfield theory, is constructed in terms of observable EM fields andco-moving local physical media parameters. Localization of tensors toobservables is introduced and justified, and a relation is obtainedconnecting tensor transforms to instantaneous Lorentz transforms forobservers in different frames. A constitutive tensor, explicitlyexpressed by the four-velocity and the local properties in co-movingframe of a linear medium, is found for the first time. Previous mistakesin confusing the tensors, in which forms the physical quantitiescombine with the non- flatness of frames to be used in covariant equationsand thus make geometrical quantities, with observables arecleared. Also a Lagrangian formulation for both lossless and lossymedia is constructed, and boundary conditions, local conservation laws,and energy momentum tensor are obtained.
The second half concerns application to motions in SRT, suchas uniform linear (hyperbolic) acceleration and steady rotation. Forthese local Maxwell equations in co-moving frames are obtained, andapproximate solutions are found for special cases. An EM wavepropagating in the direction of acceleration is studied in theaccelerating frame. The first order propagation shows a frequencyshift and amplitude change which have very simple physical significancesof instantaneous Doppler shift and photon density in mediaand which agree with familiar results in the vacuum limit. A particlemodel for this wave shows that the "mass dressed" photon is dragged bythe medium and does not follow a geodesic path. In the rotating mediumcase a plane wave scattered by a rotating sphere is solved by an integraliteration method in the laboratory frame. The scattered fieldpurely associated to the rotation of the medium is separated from theMie scattering. Its first order amplitudes are found and plotted forincidences perpendicular and parallel to the rotation axis. Particularsynunetry and shapes of scattering amplitude in the results agree withintuition and resemble radiation patterns of appropriately inducedtraveling electric and magnetic dipole sheaths.
*The contribution of EM field to gµv is neglected.
