Stationary Worldline Power Distributions

Abstract

A worldline with a time-independent spectrum is called stationary. Such worldlines are arguably the most simple motions in physics. Barring the trivially static motion, the non-trivial worldlines are uniformly accelerated. As such, a point charge moving along a stationary worldline will emit constant radiative power. The angular distribution, maximum angle scaling and Thomas precession of this power is found for all stationary worldlines including those with torsion and hypertorsion.

Unruh-like effects: effective temperatures along stationary worldlines

“…In the Nulltor case this is the Unruh temperature along a linearly uniformly accelerated trajectory, see, e.g., [1,7,8,28,[38][39][40]. For the Parator trajectory, see, e.g., [7,12,28,41]. The effective temperature in the Ultrator (circular) case was studied already in [4][5][6], and is also discussed thoroughly in the recent work [10], but the rigorous analytic results as b → κ and as κ → 0 that we present here are new.…”

“…We summarize these trajectories in table 1. The power distributions of radiation have been calculated for each of these trajectories in [12] where a point charge moving uniformly accelerated along each path emits constant radiative power.…”

Quantum Power Distribution of Relativistic Acceleration Radiation: Classical Electrodynamic Analogies with Perfectly Reflecting Moving Mirrors

“…Third, we comment on the general applicability of the power distribution of Equation ( 23). This formula applies to very general trajectories (albeit globally asymptotically sub-light speed and time-like; although this does not stop one from being able to locally compute the power distributions of the five classes of uniform acceleration, which for an electric charge will be the same form as for uniformly accelerated moving mirrors [23]. It is unclear whether the effective temperatures will also carry-over [24]).…”

“…We now have picked up a π and a Fourier transform. We plug in Equation (23), which is the time-domain Equation (24), into:…”

“…Experimental verification will be facilitated by knowing the distribution of detected radiation. Recent studies have only just solved for the five classes of uniformly accelerated trajectory distribution [23] in classical electrodynamics (effective Unruh-like temperatures have also been calculated [24]). Unfortunately, mathematically, no settled upon or convincing [25] covariant expression has yet been derived to express the power distribution in a frame-independent formulation [26].…”