General Relativistic Simulations of Accretion Disks Around Tilted Kerr Black Holes
We simulate the dynamics of self-gravitating accretion disks around tilted Kerr black holes (BH) in full 3D general relativity. For this purpose we employ the EinsteinToolkit, using the thorn McLachlan for the evolution of the spacetime via the BSSN formalism of the Einstein equations and the thorn GRHydro for the evolution of the hydrodynamics, using a 3D Cartesian mesh with adaptive mesh refinement. We investigate the effects of the tilt angle between the disk angular momentum and BH spin vector on the dynamics of these systems as the disk evolves in the tilted spacetime. By evolving the spacetime and matter fields, we are able to observe how both BH and disk react and evolve in the tilte…
Numerical relativity simulations of thick accretion disks around tilted Kerr black holes
In this work we present 3D numerical relativity simulations of thick accretion disks around tilted Kerr BH. We investigate the evolution of three different initial disk models with a range of initial black hole spin magnitudes and tilt angles. For all the disk-to-black hole mass ratios considered (0.044-0.16) we observe significant black hole precession and nutation during the evolution. This indicates that for such mass ratios, neglecting the self-gravity of the disks by evolving them in a fixed background black hole spacetime is not justified. We find that the two more massive models are unstable against the Papaloizou-Pringle (PP) instability and that those PP-unstable models remain unst…
On the dynamics of tilted black hole-torus systems
We present results from three-dimensional, numerical relativity simulations of a {\it tilted} black hole-thick accretion disc system. The simulations are analysed using tracer particles in the disc which are advected with the flow. Such tracers, which we employ in these new simulations for the first time, provide a powerful means to analyse in detail the complex dynamics of tilted black hole-torus systems. We show how its use helps to gain insight in the overall dynamics of the system, discussing the origin of the observed black hole precession and the development of a global non-axisymmetric $m=1$ mode in the disc. Our three-dimensional simulations show the presence of quasi-periodic oscil…
Numerical relativity simulations of tilted black hole-torus systems
Las fusiones de objetos compactos se encuentran entre los eventos más interesantes de la astrofísica relativista, siendo, en particular, el principal objetivo de la astronomía de ondas gravitatorias. En esta tesis investigamos los posibles estados finales de la fusión de sistemas binarios formados por agujero negro-estrella de neutrones o por dos estrellas de neutrones: discos gruesos (o toros) de acrecimiento alrededor de agujeros negros en rotación tipo Kerr. Estos sistemas agujero negro-toro se cree que constituyen el motor central de los eventos más luminosos del Universo: los llamados estallidos de rayos gamma. Nuestro conocimiento sobre la evolución y la estabilidad de estos sistemas …
Computational general relativistic force-free electrodynamics
General relativistic force-free electrodynamics is one possible plasma-limit employed to analyze energetic outflows in which strong magnetic fields are dominant over all inertial phenomena. The amazing images of black hole shadows from the galactic center and the M87 galaxy provide a first direct glimpse into the physics of accretion flows in the most extreme environments of the universe. The efficient extraction of energy in the form of collimated outflows or jets from a rotating BH is directly linked to the topology of the surrounding magnetic field. We aim at providing a tool to numerically model the dynamics of such fields in magnetospheres around compact objects, such as black holes an…
Measuring the black hole spin direction in 3D Cartesian numerical relativity simulations
We show that the so-called flat-space rotational Killing vector method for measuring the Cartesian components of a black hole spin can be derived from the surface integral of Weinberg's pseudotensor over the apparent horizon surface when using Gaussian normal coordinates in the integration. Moreover, the integration of the pseudotensor in this gauge yields the Komar angular momentum integral in a foliation adapted to the axisymmetry of the spacetime. As a result, the method does not explicitly depend on the evolved lapse $\ensuremath{\alpha}$ and shift ${\ensuremath{\beta}}^{i}$ on the respective time slice, as they are fixed to Gaussian normal coordinates while leaving the coordinate label…
Computational general relativistic force-free electrodynamics
Scientific codes are an indispensable link between theory and experiment; in (astro-)plasma physics, such numerical tools are one window into the universe's most extreme flows of energy. The discretization of Maxwell's equations - needed to make highly magnetized (astro)physical plasma amenable to its numerical modeling - introduces numerical diffusion. It acts as a source of dissipation independent of the system's physical constituents. Understanding the numerical diffusion of scientific codes is the key to classify their reliability. It gives specific limits in which the results of numerical experiments are physical. We aim at quantifying and characterizing the numerical diffusion propert…
Spontaneous creation of circularly polarized photons in chiral astrophysical systems
This work establishes a relation between chiral anomalies in curved spacetimes and the radiative content of the gravitational field. In particular, we show that a flux of circularly polarized gravitational waves triggers the spontaneous creation of photons with net circular polarization from the quantum vacuum. Using waveform catalogues we identify precessing binary black holes as astrophysical configurations that emit such gravitational radiation, and then solve the fully non-linear Einstein's equations with numerical relativity to evaluate the net effect. The quantum amplitude for a merger is comparable to the Hawking emission rate of the final black hole, and small to be directly observe…
On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method
The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. …
Quasistationary solutions of self-gravitating scalar fields around collapsing stars
Recent work has shown that scalar fields around black holes can form long-lived, quasistationary configurations surviving for cosmological time scales. Scalar fields thus cannot be discarded as viable candidates for dark matter halo models in galaxies around central supermassive black holes (SMBHs). One hypothesized formation scenario of most SMBHs at high redshift is the gravitational collapse of supermassive stars (SMSs) with masses of $\ensuremath{\sim}{10}^{5}\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$. Any such scalar field configurations must survive the gravitational collapse of a SMS in order to be a viable model of physical reality. To check for the postcollapse survival …