Extend discrete GRHD techniques to supersonic and generalized Bondi–Hoyle–Lyttleton accretion

Develop and implement the discrete spacetime general relativistic hydrodynamics formulation and Gravitas numerical framework, which are validated here for radial Bondi accretion, to cover supersonic Hoyle–Lyttleton accretion and the generalized Bondi–Hoyle–Lyttleton accretion flows onto black holes within discrete spacetimes.

Background

The paper derives and implements a formulation of general relativistic hydrodynamics tailored to discrete spacetimes, and validates it through simulations of radial (Bondi-type) accretion onto Schwarzschild and Kerr black holes using the Gravitas framework. The focus is deliberately on the spherically symmetric, radial case.

In the broader accretion literature, Bondi–Hoyle–Lyttleton accretion encompasses cases with non-zero flow velocity and potentially non-radial, supersonic regimes. The authors explicitly leave extending their discrete spacetime techniques from the radial Bondi case to the supersonic Hoyle–Lyttleton and generalized Bondi–Hoyle–Lyttleton cases as an open research problem.

References

In this article, we shall focus solely upon the case of (radial) Bondi accretion, and we leave the extension of these techniques to the supersonic Hoyle-Lyttleton case, and to the generalized Bondi-Hoyle-Lyttleton case, as an open research problem, ripe for future investigation.

— General Relativistic Hydrodynamics in Discrete Spacetime: Perfect Fluid Accretion onto Static and Spinning Black Holes  (2402.02331 - Gorard, 2024) in Introduction (Section 1)

The mechanism that orders the regimes, the confinement of the shocked gas by the curvature term at $r\sim R_{\rm acc}$, follows from the radial force balance of Eq.~(\ref{eta}), which is the same in two and three dimensions. The ordering of the regimes by $\eta$ and the formation of a torus for $\eta>1$ are therefore expected to be more robust, but whether they persist in three dimensions remains to be tested.

— Flip-Flop Shocks and Tori in Bondi-Hoyle-Lyttleton Accretion onto Rotating Kerr-Weyl Black Holes and Their Quasi-Periodic Variability  (2610.13384 - Donmez et al., 9 Oct 2026) in Section 4, Conclusions