Description
With the goal of investigating inner horizon and inner light ring instabilities of static, spherically symmetric regular black holes and black hole mimickers, respectively, we show how to emulate their corresponding spacetime possessing a radius-dependent mass function $m(r)$ in an analog-gravity platform based on a Bose-Einstein condensate (BEC). We compare the sonic and the gravitational line elements and show a correspondence between $m(r)$ and the ratio of radial flow velocity and sonic speed. This allows, in theory, to emulate the entire spacetime in the analog platform, and shows which are the condensate analog quantities for gravitational parameters like the regularization parameter $\ell$ and the ADM mass $M$ in different areas of the condensate. Resolving this correspondence relation along with the Bernoulli and continuity equation, we show how to experimentally realize the central and the asymptotic region of the gravitational spacetime in the BEC by means of a given profile $U(r)$ of the external potential and interaction strength $g(r)$, tuned by means of the Feshbach resonance with a radially varying magnetic field $B(r)$. We propose a concrete experimental setup and, using experimental values of the relevant quantities from existing BEC experiments, provide a reality-check which demonstrates the viability and realizability of our analog-gravity program.