Problemas direto e inverso em sistemas análogos da gravitação

Abstract

Analog gravity models provide an insightful source of study for the qualitative key properties of astrophysical gravitating systems, such as black holes and exotic compact objects. Unlike distant astrophysical compact objects, analog gravity systems can be properly prepared for lab-controlled table-top experiments to investigate their dynamics. Cross-sections and other scattering properties can then be assessed by careful experiments and precise measurements. This obtained data can be compared with what was expected to be gotten from the as-trophysical objects, and new physical insights can emerge. In this thesis, we report four distinct results. First, we summarize the direct problem for the linear perturbation theory of black holes and exotic horizonless compact objects, both in the astrophysical scenario and in terms of analog gravity systems. We derive the ringdown waveform signals emitted by those perturbed objects from that description. By confronting these signals, a direct signature of the exotic compact horizonless objects' core-reflectivity is detached, deriving an important smoking gun for distinguishing them from black holes. Second, we outline a semiclassical, nonparametric method that allows for the reconstruction of the effective scattering potential from the knowledge of the scattering coefficients. Third, we extend this method for energy-dependent scattering potentials to address the problem of rotating systems. Lastly, we apply this extension to study the inverse problem of analog gravity systems which admit rotation and energy-dependent boundary conditions. By extending our previous results, we provide a recipe that allows one to relate resonant transmission spectra with effective WKB-equivalent potentials and even reconstruct the boundary condition at the core of the scattering source. To demonstrate the accuracy and scope of our method, we apply it to a rotating imperfect draining vortex, which has been proposed as an analog system to astrophysical extreme com-pact objects. We conclude that the capability to reconstruct energy-dependent potentials and boundary conditions could be of interest to experimental studies of such systems.