  We explore the formation, energetics, and geometry of relativistic jets along
with the variability of their central engine. We study both fast and slowly
rotating black holes and address our simulations to active galaxy (AGN) centers
and gamma ray burst (GRB) engines. The structured jets are postulated to
account for emission properties of high energy sources across the mass scale,
launched from stellar mass black holes in GRBs and from supermassive black
holes in AGNs. Their active cores contain magnetized accretion disks and
rotation of the Kerr black hole provides a mechanism for jet launching. This
process works most effectively if the mode of accretion is magnetically
arrested (MAD). In this mode, the modulation of jets launched from the engine
is related to internal instabilities in the accretion flow that operate on
smallest time and spatial scales. As these scales are related to the
light-crossing time and the black hole gravitational radius, the universal
model of jet-disk connection is expected to scale with the black hole mass. We
investigate the jet-disk connection by means of 3D GR MHD simulations of the
MAD accretion in Kerr metric. We quantify the variability of the disk by means
of a Fourier analysis. We found that the evolution is governed by the physical
parameters of the engine such as the black hole spin and disk size as well as
its magnetization, and we applied our scenarios to typical types of sources in
AGN and GRB classes. We found that the MAD scenario is applicable to AGN
engines and supports persistent jet emission. It can also be applied to GRBs,
as it gives the variability pattern roughly consistent with observations.
However, in some cases, strong magnetic fields may lead to jet quenching, and
this effect is found to be important mainly for GRB jets. We speculate that it
may be related to the strength of magnetically driven winds from the GRB
engines.
