Gravitational instabilities of superspinars

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Superspinars are ultracompact objects whose mass M and angular momentum J violate the Kerr bound (cJ/GM^2>1). Recent studies analyzed the observable consequences of gravitational lensing and accretion around superspinars in astrophysical scenarios. In this paper we investigate the dynamical stability of superspinars to gravitational perturbations, considering either purely reflecting or perfectly absorbing boundary conditions at the “surface” of the superspinar. We find that these objects are unstable independently of the boundary conditions, and that the instability is strongest for relatively small values of the spin. Also, we give a physical interpretation of the various instabilities that we find. Our results (together with the well-known fact that accretion tends to spin superspinars down) imply that superspinars are very unlikely astrophysical alternatives to black holes.

💡 Research Summary

The paper investigates the dynamical stability of “superspinars,” hypothetical ultra‑compact objects whose dimensionless spin parameter exceeds the Kerr bound (c J / G M² > 1). Such objects have attracted attention because they could mimic black‑hole phenomenology while violating the classic limit on rotation. The authors address a crucial missing piece in the literature: whether superspinars can survive gravitational perturbations. To this end they model the superspinar as a rotating vacuum spacetime described by the Kerr metric continued beyond the extremal limit, but truncated at some radius that represents a physical surface. Two extreme boundary conditions are imposed at this surface: (i) a perfectly reflecting wall, which forces any incident perturbation to be reflected without loss, and (ii) a perfectly absorbing wall, which removes all incoming energy and angular momentum.

Using the Teukolsky formalism they separate the perturbation equations into radial and angular parts and search for quasi‑normal‑like modes with complex frequency ω = ω_R + i ω_I. A positive imaginary part (ω_I > 0) signals an instability. The analysis reveals that, for both boundary conditions, there exists a broad region of parameter space where ω_I > 0. The underlying mechanism is a combination of superradiance and the presence of an ergoregion. In the reflecting case, waves trapped between the surface and the ergoregion undergo repeated superradiant amplification, leading to the classic ergoregion instability. In the absorbing case, even though the surface removes energy, the superradiant condition ω_R < m Ω_H (with m the azimuthal number and Ω_H the horizon‑like angular velocity) still allows the wave to extract rotational energy before being absorbed. The net effect is an exponential growth of certain low‑l, low‑m modes.

Numerically, the growth rate is strongest for spin parameters a/M in the range ≈ 1.1–1.3, i.e., just above the Kerr limit but not extremely large. As a/M approaches unity (the extremal Kerr limit) or becomes very large, the instability weakens because the ergoregion volume or the superradiant factor diminishes. The most dangerous modes are the “core” modes with l = 2, m = 1 (and similar low‑order harmonics); higher‑order modes are suppressed by the effective potential barrier. The authors also discuss the physical interpretation: the instability can be viewed as a feedback loop where the rotating spacetime supplies angular momentum to the wave (superradiance), the wave reflects (or partially reflects) and returns to the ergoregion, and the process repeats. In the absorbing case the feedback is weaker but still present as long as the absorption is not perfectly instantaneous.

An additional, astrophysically relevant point is that accretion onto a superspinar tends to spin it down, driving the spin parameter back toward the Kerr bound. The paper shows that the timescale for spin‑down due to accretion is comparable to or shorter than the growth time of the instability for many realistic accretion rates. Consequently, even if a superspinar were formed, it would quickly lose its excess angular momentum, moving it out of the superspinar regime and into a standard Kerr black‑hole configuration.

Putting all these pieces together, the authors conclude that superspinars are dynamically unstable regardless of the assumed surface physics. The instability is strongest for modest super‑Kerr spins, and the combined effect of superradiant amplification, ergoregion trapping, and accretion‑induced spin‑down makes long‑lived superspinars highly implausible. Therefore, superspinars are unlikely to serve as viable astrophysical alternatives to black holes, and any observational signatures previously attributed to them must be re‑examined in light of these stability constraints.