Nonlinear processes in general relativity: from vacuum spacetimes to turbulent plasmas near compact objects

Abstract

Strong gravitational fields are well-described by Einstein’s theory of gravity. In the last decades, observational breakthroughs have supported the milestones of general relativity, stimulating increasing scientific activity. Together with observations, numerical relativity became a very important instrument to validate and extend the comprehension of such observations. In the first part of this thesis, we present new results through the full threedimensional (3D) evolution of black holes, in binary- and multiple-body systems. After a brief review of Einstein’s theory and of the "3+1" formalism adopted, we describe the Spectral FIltered Numerical Gravity CodE (SFINGE). This is a numerical code based on the Fourier decomposition, accompanied by different filtering techniques. The accuracy of the model has been validated through standard testbeds, revealing that the filtered pseudo-spectral technique is highly accurate. We evolve black hole dynamics in vacuum conditions and small domains. The gravitational wave signals have been inspected by employing both Fourier and wavelet analyses, showing net differences among the global configurations. We observe strong nonlinear emission in the case of three-black holes, which can be a template for future observational campaigns. Finally, we introduced also the presence of matter in spacetime, presenting some preliminary results of general relativistic hydrodynamics. In the second part of the thesis, we focus on the plasma in the neighboring regions of black holes, by using numerical models for plasmas in trans-relativistic regimes. We present a very comprehensive campaign of two-dimensional (2D) kinetic Particle-In-Cell (PIC) simulations of special-relativistic turbulence by using the Zeltron code. Imposing a realistic mass ratio between electrons and protons, we analyze the energization of electrons, by varying several plasma parameters. The simulations have been designed to cover several regimes of turbulence in the vicinity of compact objects. These results can find application in a wide range of astrophysical scenarios, including the accretion and the jet emission onto supermassive black holes, such as M87* and Sgr A*.