Cosmology on Simplicial Complexes

Analytical solutions of the Einstein field equations heavily rely on symmetries imposed on the underlying spacetime. Due to the complexity of these non-linear coupled partial differential equations, finding more general solutions is a difficult task. In cosmology the most considerations are based on the well known FLRW metric or on perturbations of the latter, although the observed universe departs greatly from the underlying assumptions on smaller scales.

To address this issues, the framework of Regge calculus and its possible use for cosmology is examined. In this formalism the spacetime is approximated by finite sized simplices, building a simplicial complex and upon it a numerical time evolution scheme can be constructed. An introduction to the concepts in this field is presented together with an original method to account for the dynamical effects of the cosmological constant $\Lambda$. A new numerical library is briefly described. Finally, as an application, it is shown that the time evolution of the Kasner and $\Lambda$-vacuum spacetime can be reproduced.

Numerical relativity simulations of thick accretion disks around tilted Kerr black holes

In this talk, I will present results of our recent 3D GRHD simulations of thick accretion disks around tilted Kerr black holes.  We investigate the effects of the tilt angle between the disk angular momentum vector and black hole spin on the dynamics of these systems, being particularly interested in a possible imprint of the tilt angle in the gravitational wave pattern as the torus evolves in the tilted spacetime. We find that Papalouizou-Pringle unstable models still develop the PPI when the central BH is tilted. For the models where the PPI saturates abruptly, the central BH is given a mild kick. We simulate the systems using the Einstein Toolkit, using the thorn McLachlan for the evolution of the spacetime via the BSSN formalism and the thorn GRHydro for the evolution of the hydrodynamics, using a 3D Cartesian mesh with adaptive mesh refinement (AMR).