Generalized, energy-conserving numerical simulations of particles in general relativity. II. Test particles in electromagnetic fields and GRMHD

TL;DR

This paper extends energy-conserving numerical methods for particles in general relativity to include electromagnetic forces, enabling accurate simulations of charged particles in complex astrophysical environments like black hole accretion disks.

Contribution

It introduces a Hamiltonian energy-conserving scheme for charged particles in curved spacetime with electromagnetic fields, tested against standard methods and applied to GRMHD simulations.

Findings

The new scheme conserves energy better than standard methods.

It accurately reproduces analytic solutions for particle trajectories.

Successfully applied to simulate charged particles in GRMHD environments.

Abstract

Direct observations of compact objects, in the form of radiation spectra, gravitational waves from VIRGO/LIGO, and forthcoming direct imaging, are currently one of the primary source of information on the physics of plasmas in extreme astrophysical environments. The modeling of such physical phenomena requires numerical methods that allow for the simulation of microscopic plasma dynamics in presence of both strong gravity and electromagnetic fields. In Bacchini et al. (2018) we presented a detailed study on numerical techniques for the integration of free geodesic motion. Here we extend the study by introducing electromagnetic forces in the simulation of charged particles in curved spacetimes. We extend the Hamiltonian energy-conserving method presented in Bacchini et al. (2018) to include the Lorentz force and we test its performance compared to that of standard explicit Runge-Kutta and implicit midpoint rule schemes against analytic solutions. Then, we show the application of the numerical schemes to the integration of test particle trajectories in general relativistic magnetohydrodynamic (GRMHD) simulations, by modifying the algorithms to handle grid-based electromagnetic fields. We test this approach by simulating ensembles of charged particles in a static GRMHD configuration obtained with the Black Hole Accretion Code (BHAC).