The Great Impersonation: $\mathcal{W}$-Solitons as Prototypical Black Hole Microstates

TL;DR

The paper introduces ${\cal W}$-solitons, smooth horizonless solitons in five-dimensional supergravity that share mass and charges with four-dimensional black holes but replace horizons with a Kaluza–Klein bubble. Through geodesic analysis, lensing/ray-tracing, and scalar perturbation studies, the authors show that ${\cal W}$-solitons reproduce many black-hole phenomenologies such as a single photon sphere and short-lived quasinormal modes, while exhibiting distinctive, testable deviations (e.g., reflective bubble surface, absence of echoes, and ~10–15% shifts in QNM frequencies). They find linear stability under scalar perturbations and highlight observational prospects for differentiating these horizonless microstate prototypes from classical BHs, including implications for gravitational-wave ringdown spectroscopy. The work provides a concrete, parameter-free, analytically tractable framework for horizon-scale black hole microstates with potential relevance to current and near-future observations like GW250114 and high-resolution imaging.

Abstract

We analyze a new class of static, smooth geometries in five-dimensional supergravity, dubbed $\mathcal{W}$-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 $\mathcal{W}$-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~(QNMs), 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 ${\mathcal{O}}(10\%)$ level, compatible with the recent measurement of GW250114 and potentially falsifiable in the near future. Finally, we show that $\mathcal{W}$-solitons are stable under scalar perturbations. Our results underscore the qualitative similarities between $\mathcal{W}$-solitons and black holes, reinforcing their relevance as smooth black hole microstate prototypes.

Figures (8)

• Figure 1: Properties of the photon sphere for the ${\cal W}$-soliton and the black string as functions of the charge-to-mass ratio. Top left panel: Radius of the round two-sphere at the location of the photon orbit. Top right panel: Angular momentum of photons on the orbit, which also determines the apparent size of the photon sphere as seen by an asymptotic observer. Bottom left panel: Lyapunov exponent characterizing the instability of the photon sphere. Bottom right panel: Angular velocity of photons at the photon sphere, related to the QNM frequencies.
• Figure 2: Illustration of the artificial background grids used for imaging. The observer (smaller gray point) is placed on a "celestial" sphere centered around the gravitational object (represented as a larger white sphere). For the first background, the celestial sphere is covered with a quadri-color grid of meridians and latitudes. For the second background, the sphere is entirely black except for a bright accretion disk. The disk is inclined by an angle $\pi/3$ relative to the camera-object plane and spans the radial range $[6M,7M]$. The celestial spheres have been artificially truncated here to improve visibility near the ISCO.
• Figure 3: Gravitational lensing effects of the ${\cal W}$-soliton compared to its corresponding black string. From left to right: the four different backgrounds for $Q=0$ and $Q=1.2M$. First row: imaging simulation with a quadri-color screen on the celestial sphere. Second row: imaging simulation of an artificial bright accretion disk near the ISCO.
• Figure 4: Scalar potential of the ${\cal W}$-soliton for $p = 0$ and $p \neq 0$, in regimes where the potential changes sign. The plots show $V_{\cal W}({r_*})$ from \ref{['eq:PotentialsDef']} for $k = 100$, $N = 30$, $\ell = 10$, and $(\omega R_\psi, p) = (1.03, 1)$ or $(1/3, 0)$.
• Figure 5: Ratios of the QNM frequencies for the ${\cal W}$-soliton and the black string. In the WKB approximation (solid lines), these ratios depend only on $Q/M$ and are independent of $(M,\ell,n)$. The dots are the numerical values from the direct-integration method at $\ell=2$ (up to $Q/M=1.3$), indicating an excellent agreement with WKB values, even for small $\ell$.