  In this paper, we study rotating horizon less black shells as an alternative
to Kerr black holes. We make use of Ernst's potential to solve the Einstein
equations perturbatively in the angular momentum $a$. Calculating to order
$a^6$, we find accurate predictions up to about $a=0.45$, where the quadrupole
moment is predicted to be around $1\%$ higher than its Kerr value; higher
multipole moments show deviation of the order of $\sim 10\%$. Our analysis
takes into account deformations of the black shells, and we propose that it can
be used for numerical simulations comparing gravitational waves emitted by
orbiting black shells with those emitted by orbiting black holes. In our
analysis, we make extensive use of relativistic hydrodynamics, and discover an
intricate structure of circulating flows of fluid and heat on the black shell,
sustained by the Unruh effect.
