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General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
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 quasi-normal 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
semi-classical, non-parametric 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 analog of extreme compact objects. Although the inverse problem is in
general not unique, choosing physically motivated assumptions and requiring the
validity of semi-classical theory, we demonstrate that the method provides
efficient and accurate results.
