Relativistic Maxwell-Bloch Equations with Applications to Astrophysics

TL;DR

This paper derives relativistic Maxwell-Bloch equations to describe radiative processes like maser action and superradiance in astrophysical settings, accounting for relativistic effects on timescales and coherence.

Contribution

It introduces relativistic formulations of Maxwell-Bloch and maser equations, highlighting invariance of coherence and proper transformation of radiation properties across reference frames.

Findings

Radiation response is preserved at different velocities.

Timescales and intensities transform relativistically as expected.

Coherence between emitters at different speeds remains unchanged.

Abstract

We derive relativistic Maxwell-Bloch equations for potential applications in astronomical environments, where various radiative processes are known to occur, including the maser action and Dicke's superradiance. We show that for both phenomena a radiating system's response is preserved at different relative velocities between the system's rest frame and the observer, while the relevant timescales and the radiation intensity transform as expected from relativistic considerations. We verify that the level of coherence between groups of emitters travelling at different speeds is unchanged in all reference frames. We also derive relativistic versions of the maser equations applicable in the steady-state regime.