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In this work we present 3D numerical relativity simulations of thickaccretion disks around tilted Kerr BH. We investigate the evolution of threedifferent initial disk models with a range of initial black hole spinmagnitudes and tilt angles. For all the disk-to-black hole mass ratiosconsidered (0.044-0.16) we observe significant black hole precession andnutation during the evolution. This indicates that for such mass ratios,neglecting the self-gravity of the disks by evolving them in a fixed backgroundblack hole spacetime is not justified. We find that the two more massive modelsare unstable against the Papaloizou-Pringle (PP) instability and that thosePP-unstable models remain unstable for all initial spins and tilt anglesconsidered, showing that the development of the instability is a very robustfeature of such PP-unstable disks. Our lightest model, which is the mostastrophysically favorable outcome of mergers of binary compact objects, isstable. The tilt between the black hole spin and the disk is strongly modulatedduring the growth of the PP instability, causing a partial global realignmentof black hole spin and disk angular momentum in the most massive model withconstant specific angular momentum l. For the model with non-constant l-profilewe observe a long-lived m=1 non-axisymmetric structure which shows strongoscillations of the tilt angle in the inner regions of the disk. This effectmight be connected to the development of Kozai-Lidov oscillations. Oursimulations also confirm earlier findings that the development of the PPinstability causes the long-term emission of large amplitude gravitationalwaves, predominantly for the l=m=2 multipole mode. The imprint of the BHprecession on the gravitational waves from tilted BH-torus systems remains aninteresting open issue that would require significantly longer simulations thanthose presented in this work.

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