Solving Einstein equations using deep learning

Autor:	Li, Zhi-Han, Li, Chen-Qi, Pang, Long-Gang
Rok vydání:	2023
Předmět:	General Relativity and Quantum Cosmology Nuclear Theory Physics - Computational Physics
Druh dokumentu:	Working Paper
Popis:	Einstein field equations are notoriously challenging to solve due to their complex mathematical form, with few analytical solutions available in the absence of highly symmetric systems or ideal matter distribution. However, accurate solutions are crucial, particularly in systems with strong gravitational field such as black holes or neutron stars. In this work, we use neural networks and auto differentiation to solve the Einstein field equations numerically inspired by the idea of physics-informed neural networks (PINNs). By utilizing these techniques, we successfully obtain the Schwarzschild metric and the charged Schwarzschild metric given the energy-momentum tensor of matter. This innovative method could open up a different way for solving space-time coupled Einstein field equations and become an integral part of numerical relativity. Comment: 18 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.07397 Zobrazit plný text záznamu View this record from Arxiv