A new covariant formalism for kinetic plasma simulations in curved spacetimes

TL;DR

This paper introduces a covariant guiding center formalism for kinetic plasma simulations in curved spacetimes, enabling astrophysical applications near black holes and neutron stars by overcoming previous flat-spacetime limitations.

Contribution

The authors develop a new covariant kinetic formalism that generalizes guiding center equations to arbitrary spacetimes, facilitating global plasma simulations in astrophysical environments.

Findings

Captures all known gyro-center drifts

Overcomes limitations of fast gyromotion timescales

Validated through various experiments

Abstract

Low density plasmas are characterized by a large scale separation between the gyromotion of particles around local magnetic fields and the macroscopic scales of the system, often making global kinetic simulations computationally intractable. The guiding center formalism has been proposed as a powerful tool to bridge the gap between these scales. Despite its usefulness, the guiding center approach has been formulated successfully only in flat spacetimes, limiting its applicability in astrophysical settings. Here, we present a new covariant formalism that leads to kinetic equations in the guiding center limit that are valid in arbitrary spacetimes. Through a variety of experiments, we demonstrate that our equations capture all known gyro-center drifts while overcoming one severe limitation imposed on numerical algorithms by the fast timescales of the particle gyromotion. This formalism will enable explorations of a variety of global plasma kinetic phenomena in the curved spacetimes around black holes and neutron stars.