Taking horizonless black hole mimickers out for a spin

Authors: Ulf Danielsson and Suvendu Giri Preprint number: UUITP-29/23 Abstract: In this paper, we study rotating horizon less black shells as an alternative to Kerr black holes. We make use of the Ernst method 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 enhancement in the quadrupole moment is predicted to be around $1\%$. 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.