FPIC: A new Particle-In-Cell code for stationary and axisymmetric black-hole spacetimes

Black holes in astrophysical environments are expected to be immersed in magnetized collisionless plasmas, whose electrodynamics leads to some of the powerful energetic emissions observed. To model such environments, a kinetic description is best-suited to capture the microphysics underlying the complex phenomena near such compact objects. In recent years, general-relativistic Particle-In-Cell (GRPIC) simulations have received increasing interest from the astrophysics community, becoming an excellent tool to study the immediate vicinity of the event horizons of stellar-mass and supermassive black holes. In this paper, we present a newly developed GRPIC code framework called FPIC . We describe in detail the code, which is written in Fortran and exploits parallel architectures using MPI directives. The Maxwell equations are evolved using a finite-difference time-domain solver with a leapfrog scheme, while multiple particle “pushers” are implemented for the evolution of the particles. In addition to well-known algorithms, we introduce a novel hybrid method that dynamically switches between the most appropriate scheme based on the violation of the Hamiltonian energy. We first present results for neutral particles orbiting around black holes, monitoring the evolution of the Hamiltonian error across different integration schemes. We apply our hybrid approach, showing that it is capable of achieving improved energy conservation at reduced computational cost. Results for charged particles in the presence of a magnetic field are also presented, where the interpolation plays a crucial role in maintaining Hamiltonian conservation. We then apply FPIC to investigate the Wald solution, first in electrovacuum and subsequently in plasma-filled configurations. In the latter case, particles with negative energy at infinity are present inside the ergosphere, indicating that the Penrose process is active. Finally, we present the split-monopole solution in a plasma-filled environment and successfully reproduce the Blandford-Znajek luminosity, finding very good agreement with analytical predictions.

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