We study a point scalar charge in circular orbit around a topological star, a regular, horizonless soliton emerging from dimensional compactification of Einstein-Maxwell theory in five dimensions, which could describe qualitative properties of microstate geometries for astrophysical black holes. This is the first step toward studying extreme mass-ratio inspirals around these objects. We show that when the particle probes the spacetime close to the object, the scalar-wave flux deviates significantly from the corresponding black hole case. Furthermore, as the topological star approaches the black-hole limit, the inspiral can resonantly excite its long-lived modes, resulting in sharp features in the emitted flux. Although such resonances are too narrow to produce detectable dephasing, we estimate that a year-long inspiral down to the innermost stable circular orbit could accumulate a significant dephasing for most configurations relative to the black hole case. While a full parameter-estimation analysis is needed, the generically large deviations are likely to be within the sensitivity reach of future space-based gravitational-wave detectors.

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• Alternative gravity theories
• Classical black holes
• Gravitational waves
• Gravity in dimensions other than four