A Four-Dimensional Gaussian Random Field Generator for Modeling Spatiotemporal Variability in Astrophysical Sources
Abstract
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 Matérn-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.
Versions
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BibTeX
@misc{cardenasavendano2026fourdimensional,
title = {{A Four-Dimensional Gaussian Random Field Generator for Modeling Spatiotemporal Variability in Astrophysical Sources}},
author = {Alejandro Cárdenas-Avendaño and Diego Rubiera-Garcia and Frederic H. Vincent},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.16576},
eprint = {2607.16576},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16576},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Four-Dimensional Gaussian Random Field Generator for Modeling Spatiotemporal Variability in Astrophysical Sources
AU - Alejandro Cárdenas-Avendaño
AU - Diego Rubiera-Garcia
AU - Frederic H. Vincent
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2607.16576
UR - https://arxiv.org/abs/2607.16576
AB - 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 Matérn-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.
ER -