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 towards 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.

Cet article explore les excursions dans le temps et leurs implications.

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