With the success of static black-hole imaging, the next frontier is the dynamic and 3D imaging of black holes. Recovering the dynamic 3D gas near a black hole would reveal previously-unseen parts of the universe and inform new physics models. However, only sparse radio measurements from a single viewpoint are possible, making the dynamic 3D reconstruction problem significantly ill-posed. Previously, BH-NeRF addressed the ill-posed problem by assuming Keplerian dynamics of the gas, but this assumption breaks down near the black hole, where the strong gravitational pull of the black hole and increased electromagnetic activity complicate fluid dynamics. To overcome the restrictive assumptions of BH-NeRF, we propose PI-DEF, a physics-informed approach that uses differentiable neural rendering to fit a 4D (time + 3D) emissivity field given EHT measurements. Our approach jointly reconstructs the 3D velocity field with the 4D emissivity field and enforces the velocity as a soft constraint on the dynamics of the emissivity. In experiments on simulated data, we find significantly improved reconstruction accuracy over both BH-NeRF and a physics-agnostic approach. We demonstrate how our method may be used to estimate other physics parameters of the black hole, such as its spin.

翻译：随着静态黑洞成像的成功，下一个前沿方向是黑洞的动态与三维成像。恢复黑洞附近的动态三维气体结构将揭示宇宙中此前不可见的部分，并为新的物理模型提供信息。然而，由于只能从单一视角获得稀疏的射电测量数据，动态三维重建问题呈现出显著的不适定性。此前，BH-NeRF通过假设气体符合开普勒动力学来处理该不适定问题，但这一假设在黑洞附近区域失效——因为黑洞强大的引力拖拽和增强的电磁活动使得流体动力学复杂化。为突破BH-NeRF的限制性假设，我们提出PI-DEF：一种基于物理信息的方法，利用可微神经渲染技术，根据EHT测量数据拟合四维（时间+三维）发射率场。该方法联合重建三维速度场与四维发射率场，并将速度作为发射率动力学的软约束。在模拟数据实验中，我们发现相较于BH-NeRF及物理无关方法，本方法显著提升了重建精度。我们还展示了如何运用该方法估算黑洞的自转等其他物理参数。