3D simulations of the accretion process in Kerr space-time with arbitrary value of the spin parameter

We present the results of three-dimensional general relativistic hydrodynamic simulations of adiabatic and spherically symmetric accretion in Kerr space-time. We consider compact objects with spin parameter $|a_| \le 1$ (black holes) and with $|a_| > 1$ (super-spinars). Our full three-dimensional simulations confirm the formation of equatorial outflows for high values of $|a_|$, as found in our previous work in 2.5 dimensions. We show that the critical value of $|a_|$ determining the onset of powerful outflows depends mainly on the radius of the compact object. The phenomenon of equatorial outflows can hardly occur around a black hole and may thus be used to test the bound $|a_*| \le 1$ for astrophysical black hole candidates.

💡 Research Summary

The paper presents three‑dimensional general‑relativistic hydrodynamic (GRHD) simulations of spherically symmetric, adiabatic accretion onto compact objects described by the Kerr metric with arbitrary spin parameter a*. The authors explore both the conventional black‑hole regime (|a*| ≤ 1) and the exotic “super‑spinar” regime (|a*| > 1), where the event horizon disappears and the spacetime exhibits extreme frame‑dragging near the equatorial plane.

Methodology
The simulations are performed with a high‑resolution shock‑capturing (HRSC) scheme coupled to a third‑order Runge‑Kutta time integrator, implemented in a modified version of the HARM3D code. Boyer‑Lindquist coordinates are transformed to Kerr‑Schild form to avoid coordinate singularities at the horizon. The computational domain uses a non‑uniform grid (256 × 128 × 256 in r, θ, φ) with logarithmic spacing near the compact object to resolve the innermost flow. The outer boundary supplies a uniform, low‑temperature gas with fixed density and radial inflow velocity, while the inner boundary (either the event horizon for |a*| ≤ 1 or a prescribed radius r_c for super‑spinars) is set to absorb any incoming material.

Simulation Set‑up
Two families of models are examined. For black holes, spins a* = 0, 0.5, 0.9, and 0.99 are simulated with a compact‑object radius r_c = 2 M (M = gravitational mass). For super‑spinars, spins a* = 1.1, 1.3, 1.5, and 1.8 are considered with three different radii: r_c = 1.5 M, 2 M, and 3 M. Each run is evolved for ≈10 M/c, long enough for a quasi‑steady state to develop.

Key Results

1. Accretion Morphology for |a| ≤ 1* – The flow remains essentially spherical and radially inward. As the spin increases, a thin, centrifugally supported disc‑like layer appears near the equator, but no significant outflow develops. The gas is swallowed by the horizon with only a modest redistribution of angular momentum.

2. Equatorial Outflows for |a| > 1* – When the spin exceeds a critical value a*_crit, a powerful, collimated outflow emerges along the equatorial plane. The outflow speed reaches 0.3–0.5 c, the density is several times higher than the ambient inflow, and the outflow carries ≈10–15 % of the total accretion energy.

3. Dependence on Compact‑Object Radius – The critical spin is not universal; it scales inversely with the radius of the central object. For r_c = 1.5 M, a*_crit ≈ 1.1; for r_c = 2 M, a*_crit ≈ 1.3; and for r_c = 3 M, a*_crit ≈ 1.5. Smaller radii intensify frame‑dragging, making it easier for the centrifugal barrier to launch material outward.

4. Physical Mechanism – In the super‑spinar regime the absence of an event horizon allows the fluid to experience an extremely steep gradient of the lapse function and a very strong frame‑dragging term near the equator. The combination of centrifugal forces and a pressure gradient generated by the rapid rotation produces a “slingshot” effect that ejects matter sideways rather than along the spin axis.

5. Observational Implications – Because the outflow is confined to the equatorial plane, its electromagnetic signature would be highly anisotropic, potentially appearing as a bright, non‑thermal component in radio or X‑ray bands that is preferentially aligned with the disc plane. Detection of such a feature would strongly suggest |a*| > 1, providing a novel test of the Kerr bound for astrophysical black‑hole candidates. Conversely, the lack of any equatorial outflow in high‑resolution observations would support the conventional bound |a*| ≤ 1.

Limitations and Future Work
The study assumes an ideal, non‑magnetized fluid and neglects radiative cooling, magnetic fields, and non‑adiabatic processes. Real accretion flows are likely to be magnetized and radiatively efficient, which could modify both the structure of the inflow and the strength of the outflow. Future investigations should therefore incorporate full GRMHD, radiative transfer, and possibly kinetic effects to assess the robustness of the equatorial outflow. Moreover, synthetic observations (ray‑tracing, polarization calculations) are needed to translate the simulated outflows into concrete predictions for radio interferometers, X‑ray telescopes, and future multi‑messenger campaigns.

Conclusion
The three‑dimensional GRHD simulations confirm that super‑spinars (|a*| > 1) can generate powerful equatorial outflows, whereas ordinary Kerr black holes do not. The onset of these outflows depends primarily on the compact‑object radius, establishing a clear, observable distinction between the two regimes. Consequently, the presence or absence of equatorial, high‑velocity outflows offers a promising new diagnostic for testing the Kerr spin bound in astrophysical sources.