Bound and Radiation Fields in the Rindler Frame

The energy-momentum tensor of the Li\'enard-Wiechert field is split intobound and emitted parts in the Rindler frame, by generalizing the reasoning ofTeitelboim applied in the inertial frame. Our analysis proceeds by invoking theconcept of ``energy'' defined with respect to the Killing vector field attachedto the frame. We obtain the radiation formula in the Rindler frame (the Rindlerversion of the Larmor formula), and it is found that the radiation power isproportional to the square of acceleration $\alpha^\mu$ of the charge relativeto the Rindler frame. This result leads us to split the Li\'enard-Wiechertfield into a part II', which is linear in $\alpha^\mu$, and a part I', which isindependent of $\alpha^\mu$. By using these, we split the energy-momentumtensor into two parts. We find that these are properly interpreted as theemitted and bound parts of the tensor in the Rindler frame. In ouridentification of radiation, a charge radiates neither in the case that thecharge is fixed in the Rindler frame, nor in the case that the charge satisfiesthe equation $\alpha^\mu=0$. We then investigate this equation. We considerfour gedanken experiments related to the observer dependence of the concept ofradiation.Comment: 30 pages 2 figure