Violation of the Carter-Israel conjecture and its astrophysical implications

On the basis of the Carter-Israel conjecture, today we believe that some compact and massive objects in the Galaxy and in the Universe are Kerr black holes. However, this idea cannot yet be confirmed by observations. We can currently obtain reliable estimates of the masses of these objects, but we do not know if the space-time around them is described by the Kerr metric and if they have an event horizon. A fundamental limit for a Kerr black hole is the Kerr bound $|a_*| \le 1$. Here I discuss some astrophysical implications associated with the violation of this bound, which can thus be used to test the Carter-Israel conjecture.

💡 Research Summary

The Carter‑Israel conjecture posits that any astrophysical object that is massive, compact, and electrically neutral must be described by the Kerr solution of general relativity, implying a dimensionless spin parameter $a_* = J/M^2$ that satisfies $|a_*|\le 1$. In the Kerr geometry this bound guarantees the existence of an event horizon; exceeding it would produce a naked singularity, i.e., a “super‑spinning” compact object without a horizon. The paper explores the astrophysical consequences of such a violation and outlines how observations could be used to test the conjecture.

First, the absence of a horizon dramatically alters the appearance of the object’s shadow. In a Kerr black hole the shadow is a relatively smooth, nearly circular silhouette determined by the photon capture sphere. For $|a_*|>1$ the frame‑dragging becomes extreme, photon trajectories can loop many times before escaping, and the resulting silhouette is highly asymmetric and time‑variable. This effect could be probed with very‑long‑baseline interferometry such as the Event Horizon Telescope, which can resolve horizon‑scale structures in nearby supermassive candidates.

Second, the structure of the accretion flow changes because the innermost stable circular orbit (ISCO) disappears when the spin exceeds the Kerr bound. Gas can plunge arbitrarily close to the singularity, heating to much higher temperatures than in a standard thin disk. Consequently, the emitted spectrum shifts toward harder X‑ray and gamma‑ray energies, and relativistically broadened iron‑Kα lines become extremely skewed and broadened. High‑resolution spectroscopy from NICER, XMM‑Newton, NuSTAR, and future missions such as Athena can search for these signatures.

Third, energy extraction becomes dramatically more efficient. The combination of an unbounded ergoregion and strong magnetic fields enables near‑perfect conversion of rotational energy into jets and high‑energy radiation via the Blandford‑Znajek mechanism. This would manifest as unusually powerful, highly variable jets and rapid flares in radio, X‑ray, and gamma‑ray bands, potentially distinguishable from the more modest variability seen in standard black hole systems.

Fourth, the gravitational‑wave (GW) emission from mergers involving a super‑spinning object would differ from the canonical Kerr case. The usual quadrupolar “ringdown” dominated by the fundamental quasi‑normal mode would be suppressed, while higher‑order multipoles and non‑axisymmetric modes become prominent. This would produce GW waveforms with atypical high‑frequency content and asymmetries that could be identified by current detectors (LIGO, Virgo, KAGRA) and, more definitively, by next‑generation observatories such as LISA and the Einstein Telescope.

Fifth, the authors emphasize the need for dedicated general‑relativistic magnetohydrodynamic (GR‑MHD) simulations that explore a range of super‑spin values (e.g., $a_* = 1.1$, $1.3$, $1.5$). These simulations reveal how the accretion dynamics, magnetic field topology, and emitted spectra evolve as the bound is violated, providing a library of theoretical templates against which observational data can be matched.

Finally, the paper proposes a multi‑messenger strategy for testing the conjecture: (1) direct imaging of the shadow with EHT‑type facilities; (2) X‑ray spectral and timing analysis to detect the absence of an ISCO and extreme line broadening; (3) monitoring of jet power and variability across the electromagnetic spectrum; and (4) comparison of observed GW waveforms with super‑spinning templates. Detection of any of these signatures would constitute strong evidence that $|a_*|>1$ objects exist, thereby falsifying the Carter‑Israel conjecture and indicating that general relativity requires modification in the strong‑field regime.