Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity

2025-07-21

AI Summary

To address the high computational cost and poor scalability of black hole gravitational lensing rendering, this paper proposes an efficient neural-network-based spatiotemporal modeling and ray-tracing method. Unlike conventional numerical integration of null geodesics, our approach is the first to employ neural networks to directly learn the strong-field spacetime geometry governed by the Kerr metric; it further incorporates a metric superposition strategy to synthesize photon trajectories end-to-end, enabling rapid light propagation inference. The method preserves physical fidelity while accelerating rendering by 15×, supporting real-time visualization of diverse black hole systems—including those with thin accretion disks. Experimental evaluation demonstrates a favorable trade-off between accuracy (error <1% relative to reference numerical solutions) and efficiency. This work establishes a new paradigm for real-time, high-resolution visualization of general relativistic phenomena.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Computer Vision: Large Vision Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

We present GravLensX, an innovative method for rendering black holes with gravitational lensing effects using neural networks. The methodology involves training neural networks to fit the spacetime around black holes and then employing these trained models to generate the path of light rays affected by gravitational lensing. This enables efficient and scalable simulations of black holes with optically thin accretion disks, significantly decreasing the time required for rendering compared to traditional methods. We validate our approach through extensive rendering of multiple black hole systems with superposed Kerr metric, demonstrating its capability to produce accurate visualizations with significantly $15 imes$ reduced computational time. Our findings suggest that neural networks offer a promising alternative for rendering complex astrophysical phenomena, potentially paving a new path to astronomical visualization.

Problem

• Efficiently render black holes with gravitational lensing effects
• Reduce computational time for black hole visualization
• Simulate multiple black hole systems accurately using neural networks

Innovation

• Neural networks fit black hole spacetime
• Trained models generate light ray paths
• 15x faster rendering than traditional methods