Inverse problem of analog gravity systems

Abstract: Analog gravity models of black holes and exotic compact objects provide a unique opportunity to study key properties of such systems in controlled laboratory environments. In contrast to astrophysical systems, analog gravity systems can be prepared carefully and their dynamical aspects thus investigated in unprecedented ways. While gravitational wave scattering properties of astrophysical compact objects are more connected to quasinormal modes, laboratory experiments can also access the transmission and reflection coefficients, which are otherwise mostly relevant for Hawking radiation related phenomena. In this work, we report two distinct results. First, we outline a semiclassical, nonparametric method that allows for the reconstruction of the effective perturbation potential from the knowledge of transmission and reflection coefficients for certain types of potentials in the Schr\"odinger wave equation admitting resonant tunneling. Second, we show how to use our method by applying it to an imperfect draining vortex, which has been suggested as an analog of extreme compact objects. Although the inverse problem is, in general, not unique, choosing physically motivated assumptions and requiring the validity of semiclassical theory, we demonstrate that the method provides efficient and accurate results.