A method of incorporating general relativity in electromagnetic particle-in-cell code

TL;DR

This paper introduces an algorithm that integrates general relativity into electromagnetic particle-in-cell simulations by incorporating tensor form Maxwell's equations, applicable to Schwarzschild space-time, and employs advanced numerical methods for particle dynamics.

Contribution

It presents a novel method to include general relativistic effects in electromagnetic PIC codes, enabling more accurate simulations near massive objects.

Findings

Successfully incorporates tensor form Maxwell's equations into PIC code.

Uses fourth-order Runge-Kutta for particle motion integration.

Adapts to Schwarzschild space-time for non-spinning masses.

Abstract

An algorithm is presented that incorporates the tensor form of Maxwell's equations in a general relativistic electromagnetic particle-in-cell code. The code simplifies to Schwartzschild space-time for a non-spinning central mass. The particle advance routine uses a fourth-order Runge-Kutta algorithm to integrate the four-velocity form of Lorentz force. The current density is calculated using the curved space-time of the metric.