Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole

Shuyang Xiang

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arXiv · 2506.00951

Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole

Shuyang Xiang

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Abstract

We introduce a Physics-Informed Neural Networks(PINN) to solve a relativistic Burgers equation in the exterior domain of a Schwarzschild black hole. Our main contribution is a PINN architecture that is able to simulate shock wave formations in such curved spacetime, by training a shock-aware network block and introducing a Godunov-inspired residuals in the loss function. We validate our method with numerical experiments with different kinds of initial conditions. We show its ability to reproduce both smooth and discontinuous solutions in the context of general relativity.

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Shuyang Xiang. 2025-06-01. Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole. https://arxiv.org/abs/2506.00951

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