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    W-solitons as prototypical black hole microstates

    Alexandru Dima1,2,*, Pierre Heidmann3,†, Marco Melis1,2,‡, Paolo Pani1,2,§, and Gela Patashuri3,∥

    • *Contact author: alexandru.dima@uniroma1.it
    • †Contact author: heidmann.5@osu.edu
    • ‡Contact author: marco.melis@uniroma1.it
    • §Contact author: paolo.pani@uniroma1.it
    • ∥Contact author: patashuri.1@osu.edu

    Phys. Rev. D 112, 124056 – Published 15 December, 2025

    DOI: https://doi.org/10.1103/2wcq-4xny

    Abstract

    We analyze a new class of static, smooth geometries in five-dimensional supergravity, dubbed W-solitons. They carry the same mass and charges as four-dimensional Reissner-Nordström-like black holes but replace the horizon with a Kaluza-Klein bubble supported by electromagnetic flux. These solutions provide analytically tractable prototypes of black hole microstates in supergravity, including a new, relevant neutral configuration involving a massless axion field. Focusing on photon scattering and scalar perturbations, we compute their key observables, aiming to identify mesoscopic observables. We find that W-solitons feature a single photon sphere, qualitatively similar to that of the black hole but with quantitative differences. They have only short-lived quasinormal modes, as black holes, while long-lived echo modes seen in other ultracompact horizonless objects are absent. As a result, the ringdown closely resembles that of a black hole while still showing sizable deviations. The latter are at the O(10%) level, compatible with the recent measurement of GW250114 and potentially falsifiable in the near future. Finally, we show that W-solitons are stable under scalar perturbations. Our results underscore the qualitative similarities between W-solitons and black holes, reinforcing their relevance as smooth black hole microstate prototypes.

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