Feb 23: Joonas Nättilä (KTH Royal Institute of Technology and Stockholm University)

"Relativistic plasma in silico - towards full 6D kinetic simulations"

Relativistic plasma is ubiquitous in astrophysics. Physically it can be studied by using the so-called Vlasov/Boltzmann equation that describes how the 6D (i.e., 3D3V) phase space of the plasma evolves. In my talk I will discuss our current efforts in building a general open source set of tools for simulating such systems known as the plasma-toolkit code. The toolkit is build on top of a new massively parallel grid infrastructure that can harness the next-generation exascale computing resources. In order to deal with the immense memory consumption of the full 6D phase space, the current Vlasov solver is designed to have aggressive adaptive mesh refinement capabilities both in configuration and momentum space. These new computational advances allow us to progress into a new era of simulating relativistic kinetic plasma from first principles in full 6D. I will end my talk by presenting some of our first physical results from running the toolkit in 1D3V.

Jan 26: Bart Ripperda and Fabio Bacchini (KU Leuven)

"Generalized, energy-conserving numerical integration of geodesics in general relativity"

The numerical integration of particle trajectories in curved spacetimes is fundamental for obtaining realistic models of the particle dynamics around massive compact objects such as black holes and neutron stars. Generalized algorithms capable of handling generic metrics are required for studies of both standard spacetimes Schwarzschild and Kerr metrics) and non-standard spacetimes (e.g. Schwarzschild metric plus non-classical perturbations or multiple black hole metrics). The most commonly employed explicit numerical schemes (e.g. Runge-Kutta) are incapable of producing highly accurate results at critical points, e.g. in the regions close to the event horizon where gravity causes extreme curvature of the spacetime, at an acceptable computational cost. Here, we describe a generalized algorithm for the numerical integration of time-like (massive particles) and null (photons) geodesics in any given 3+1 split spacetime. We introduce a new, exactly energy-conserving implicit integration scheme based on the preservation of the underlying Hamiltonian, and we compare its properties with a standard fourth-order Runge-Kutta explicit scheme and an implicit midpoint scheme. We test the numerical performance of the three schemes against analytical solutions of test particle and photon orbits in Schwarzschild and Kerr spacetimes. We also prove the versatility of our framework in handling more exotic metrics such as Morris-Thorne wormholes and quantum-perturbed Schwarzschild black holes. The generalized approach is also discussed in the perspective of future extensions to more complex particle dynamics, e.g. the addition of the Lorentz force acting on charged particles.

## Feb 23: Joonas Nättilä (KTH Royal Institute of Technology and Stockholm University)

## "Relativistic plasma in silico - towards full 6D kinetic simulations"

Relativistic plasma is ubiquitous in astrophysics. Physically it can be studied by using the so-called Vlasov/Boltzmann equation that describes how the 6D (i.e., 3D3V) phase space of the plasma evolves. In my talk I will discuss our current efforts in building a general open source set of tools for simulating such systems known as the plasma-toolkit code. The toolkit is build on top of a new massively parallel grid infrastructure that can harness the next-generation exascale computing resources. In order to deal with the immense memory consumption of the full 6D phase space, the current Vlasov solver is designed to have aggressive adaptive mesh refinement capabilities both in configuration and momentum space. These new computational advances allow us to progress into a new era of simulating relativistic kinetic plasma from first principles in full 6D. I will end my talk by presenting some of our first physical results from running the toolkit in 1D3V.## Jan 26: Bart Ripperda and Fabio Bacchini (KU Leuven)

## "Generalized, energy-conserving numerical integration of geodesics in general relativity"

The numerical integration of particle trajectories in curved spacetimes is fundamental for obtaining realistic models of the particle dynamics around massive compact objects such as black holes and neutron stars. Generalized algorithms capable of handling generic metrics are required for studies of both standard spacetimes Schwarzschild and Kerr metrics) and non-standard spacetimes (e.g. Schwarzschild metric plus non-classical perturbations or multiple black hole metrics). The most commonly employed explicit numerical schemes (e.g. Runge-Kutta) are incapable of producing highly accurate results at critical points, e.g. in the regions close to the event horizon where gravity causes extreme curvature of the spacetime, at an acceptable computational cost. Here, we describe a generalized algorithm for the numerical integration of time-like (massive particles) and null (photons) geodesics in any given 3+1 split spacetime. We introduce a new, exactly energy-conserving implicit integration scheme based on the preservation of the underlying Hamiltonian, and we compare its properties with a standard fourth-order Runge-Kutta explicit scheme and an implicit midpoint scheme. We test the numerical performance of the three schemes against analytical solutions of test particle and photon orbits in Schwarzschild and Kerr spacetimes. We also prove the versatility of our framework in handling more exotic metrics such as Morris-Thorne wormholes and quantum-perturbed Schwarzschild black holes. The generalized approach is also discussed in the perspective of future extensions to more complex particle dynamics, e.g. the addition of the Lorentz force acting on charged particles.