A Four-Dimensional Gaussian Random Field Generator for Modeling Spatiotemporal Variability in Astrophysical Sources

Semi-analytic models of black-hole movies require both an emitting flow prescription and a time-dependent source variability. Existing prescriptions are often limited to either equatorial emission or time-independent sources. In this work we present a unified model for these two ingredients. First, we prescribe an off-equatorial, nongeodesic Kerr fluid rotation law by lifting an equatorial specific-angular-momentum profile to cylindrical surfaces, setting the polar component of the four-velocity to zero, normalizing the flow with the full Kerr metric at the spacetime point, and retaining the option to recover a geodesic-like plunging prescription when needed. Second, we use this velocity as the disk advection field in a four-dimensional inhomogeneous, anisotropic Mat\'ern-like Gaussian random field. We provide a parametrized model for a torus-like disk and a central jet through a single composite correlation tensor. The resulting effective model is an implementation-ready prescription for time-dependent thick-disk and disk-jet emission for relativistic studies.