Horizonless black hole mimickers with spin

Abstract: 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.