Bound and Radiation Fields in the Rindler Frame

TL;DR

This paper generalizes the concept of radiation and bound fields for an accelerated charge in the Rindler frame, deriving a Rindler-specific Larmor formula and analyzing observer-dependent radiation phenomena.

Contribution

It extends the split of electromagnetic fields into bound and emitted parts to the Rindler frame, providing a new radiation formula and insights into observer-dependent radiation.

Findings

Radiation power in the Rindler frame is proportional to the square of the charge's acceleration relative to the frame.

The electromagnetic field can be split into parts linear and independent of acceleration, corresponding to emitted and bound fields.

A charge does not radiate if it is fixed in the Rindler frame or satisfies ^=0.

Abstract

The energy-momentum tensor of the Li\'enard-Wiechert field is split into bound and emitted parts in the Rindler frame, by generalizing the reasoning of Teitelboim applied in the inertial frame. Our analysis proceeds by invoking the concept of ``energy'' defined with respect to the Killing vector field attached to the frame. We obtain the radiation formula in the Rindler frame (the Rindler version of the Larmor formula), and it is found that the radiation power is proportional to the square of acceleration $\alpha^\mu$ of the charge relative to the Rindler frame. This result leads us to split the Li\'enard-Wiechert field into a part II', which is linear in $\alpha^\mu$, and a part I', which is independent of $\alpha^\mu$. By using these, we split the energy-momentum tensor into two parts. We find that these are properly interpreted as the emitted and bound parts of the tensor in the Rindler frame. In our identification of radiation, a charge radiates neither in the case that the charge is fixed in the Rindler frame, nor in the case that the charge satisfies the equation $\alpha^\mu=0$. We then investigate this equation. We consider four gedanken experiments related to the observer dependence of the concept of radiation.