  Realistic accretion disk models require a number of ingredients, including
viscous fluids, electromagnetic fields and general relativistic corrections.
Close to the innermost stable circular orbit (ISCO) the latter can be
appreciable and (quasi-)Newtonian approximations become unreliable. This is
particularly true for nearly extremal black holes like GRS 1915+105, where the
ISCO almost coincides with the black hole horizon. To describe the physics
close to the ISCO adequately in a simplified model we approximate the nearly
extremal Kerr geometry by the near-horizon extremal Kerr geometry and construct
in this background relativistic viscous fluid solutions with electromagnetic
fields. We discuss some applications of our solutions and possible relations to
the Kerr/CFT correspondence.
