| Summary: | We present a review of the influence of cosmic repulsion and external magnetic fields on accretion disks rotating around rotating black holes and on jets associated with these rotating configurations. We consider both geometrically thin and thick disks. We show that the vacuum energy represented by the relic cosmological constant strongly limits extension of the accretion disks that is for supermassive black holes comparable to extension of largest galaxies, and supports collimation of jets at large distances from the black hole. We further demonstrate that an external magnetic field crucially influences the fate of ionized Keplerian disks causing creation of winds and jets, enabling simultaneously acceleration of ultra-high energy particles with energy up to <inline-formula> <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>21</mn> </msup> </semantics> </math> </inline-formula> eV around supermassive black holes with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>M</mi> <mo>∼</mo> <msup> <mn>10</mn> <mn>10</mn> </msup> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </semantics> </math> </inline-formula> surrounded by sufficiently strong magnetic field with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>B</mi> <mo>∼</mo> <msup> <mn>10</mn> <mn>4</mn> </msup> </mrow> </semantics> </math> </inline-formula> G. We also show that the external magnetic fields enable existence of “levitating” off-equatorial clouds or tori, along with the standard equatorial toroidal structures, if these carry a non-vanishing, appropriately distributed electric charge.
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