Spontaneous charge separation in accelerating relativistic plasmas

TL;DR

This paper derives a fundamental PDE describing electrothermal stratification in relativistically accelerated plasmas, revealing electric field behaviors independent of conductivity, with solutions in accelerated boxes and near black holes.

Contribution

It introduces a first-principles derivation of a PDE for electrothermal effects in relativistic plasmas under acceleration, connecting classical effects with curved spacetime scenarios.

Findings

Electric fields in accelerating plasmas are independent of conductivity.

Derived PDE governs electrothermal stratification in relativistic plasmas.

Solutions provided for plasmas in accelerated boxes and near black holes.

Abstract

The Stewart-Tolman effect posits that accelerating conductors exhibit both charge separation and rest-frame electric fields (``inertia of charge''), while the Ehrenfest-Tolman effect states that acceleration induces temperature gradients (``inertia of heat''). We study the interplay of these effects in thermodynamic equilibrium. Specifically, we derive from first principles a partial differential equation governing the electrothermal stratification of a fully ionized plasma in equilibrium under irrotational relativistic accelerations in curved spacetime. We then solve it in two settings: a plasma enclosed in a uniformly accelerated box, and a plasma shell suspended above a black hole horizon. The resulting electric fields are found not to depend on the electric conductivity of the medium.