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In this talk I will discuss a class of compact objects called ``topological stars”. These consist in regular and horizonless solutions to five-dimensional Einstein-Maxwell theory, which resemble static BHs upon reduction to four dimensions. These mimickers are particularly interesting as they can be viewed as a classical toy model of quantum black hole microstates, such as those proposed in the “fuzzball” program in string theory.
After introducing the spacetime solution, I will summarize our latest results concerning the linear response of topological stars, with a focus on their characteristic spectrum, gravitational wave echoes and (linear) stability.