Image of a time-dependent rotating regular black hole

TL;DR

This paper introduces a novel stochastic modeling framework using spatio-temporal generalized random fields to simulate and analyze the dynamic imaging signatures of rotating regular black holes, incorporating physical effects like light-travel time.

Contribution

It extends the Matérn field formalism to spatio-temporal domains with anisotropic structures, enabling efficient, realistic simulations of black hole accretion and shadow dynamics.

Findings

Reproduces the dynamic shift of the bright ring in M87* images.

Incorporates light-travel time effects for realistic temporal smearing.

Maintains statistical consistency with GRMHD simulations.

Abstract

In this study, we develop a modeling framework based on spatio-temporal generalized random fields to simulate the time-evolving accretion flows and their associated imaging signatures around rotating regular black holes. We extend the Mat\'ern field formalism to the spatio-temporal domain and introduce a locally anisotropic tensor structure \(\Lambda(\mathbf{x})\), which encodes direction-dependent correlation scales motivated by Keplerian velocity fields, thereby generating physically informed perturbation structures. Coupled with a computationally efficient light ray-tracing scheme, this framework produces a sequence of time-resolved images of regular black hole shadow and accretion structures. By incorporating light-travel time effects, we identify significant temporal smearing of features within strongly lensed regions and rapidly varying sources, thus enhancing the physical realism of the modeling. Comparison with existing general relativistic magnetohydrodynamic simulations demonstrates that our stochastic generative model maintains statistical consistency while offering substantial computational efficiency. Moreover, the simulated results reproduce the dynamic positional shift of the bright ring structure observed in M87$^{*}$, providing theoretical support for interpreting its time-variable images.