Black Hole Dynamics from Vacuum Spacetime to Surrounding Turbulent Plasmas

Abstract

The nonlinear behavior of black holes, governed by the Einstein field equations, cou- pled with the turbulent dynamics of plasma in relativistic regimes, constitutes the cornerstone of both general relativity and high-energy astrophysics. In this thesis, we employ advanced numerical simulations and cutting-edge techniques in numer- ical relativity and plasma physics to investigate these extreme systems and probe the intricate nonlinear interactions between black holes and relativistic plasmas. The investigation begins with simulations of black hole systems in vacuum space- times, using the 3+1 formalism to explore both binary and multi-body interactions. The three-body problem is examined by transitioning from Newtonian mechanics to general relativity. In the classical framework, the interactions are modeled in a typ- ically chaotic configuration, identifying extreme gravitational interactions (EGIs) as transients characterized by complex and highly energetic dynamics. We concentrate on selecting these EGIs as initial data for the general relativistic case, performing a series of numerical relativity simulations to establish a comprehensive set of cases. The analysis of three-body black hole dynamics reveals intricate gravitational wave- forms, which are crucial for interpreting observational data and refining detection strategies. Within the 3+1 framework and in the presence of matter, a novel loga- rithmic formulation has been developed to enhance numerical stability in scenarios characterized by steep gradients, such as those found in stellar atmospheres. Pre- liminary applications of this formulation include the propagation of classical sound waves and the study of the Kelvin-Helmholtz instability. In the second part, we perform simulations using the BHAC code within theGRMHD framework to model the accreting plasma flow near black holes. These simulations provide significant insights into the behavior of matter in magnetically dominated regions, such as those surrounding Sgr A* and M87*, bridging theoretical models with observational data and offering new perspectives on high-energy astrophysi- cal processes, including jet formation, accretion mechanisms, and magnetic recon- nection. Our results demonstrate the presence of a strong turbulent cascade that transfers energy from large (inhomogeneous) accretion scales down to smaller (ho- mogeneous) lengths. This process, therefore, may conDue to the cross-scale cascade, our focus ultimately shifts to local plasma be- havior, where we explore fully kinetic plasma turbulence through high-resolution, direct numerical simulations based on the PIC method. These simulations incor- porate realistic mass ratios between particle species, allowing for a detailed exam- ination of particle acceleration mechanisms within plasma turbulence. We observe the formation of long-lived vortices with profiles typical of macroscopic, magneti- cally dominated force-free states. Inspired by the Harris pinch model for inhomo- geneous equilibria, we describe these metastable solutions using a self-consistent kinetic model in a cylindrical coordinate system centered on a representative vortex, starting from an explicit form of the particle velocity distribution function. Turbu- lence is mediated by these long-lived structures, accompanied by transients in which such vortices merge and self-similarly form new metastable equilibria. For future re- search, we plan to broaden the scope of this investigation by including positrons as a third particle species, enabling a more comprehensive analysis of multi-species plasma behavior and elucidating the dominant processes governing energy transfer, particle energization, and the resulting electromagnetic emissions.tinue to kinetic scales, where collisionless, relativistic physics becomes dominant.