Physics-Informed Neural Networks for Static Black-Hole Exterior Metrics: Charge and Cosmological-Constant Sweeps
Year: 2026
Type: preprint
Abstract: We apply physics-informed neural networks (PINNs) to recover the time-time component of static, spherically symmetric black-hole exterior metrics from a reduced ordinary differential equation (ODE). Inspired by recent work on solving Einstein field equations with deep learning~\cite{Li2023}, we encode the vacuum/charged exterior through a residual loss and an asymptotic boundary constraint---not by embedding analytic metric terms such as $2M/r$ directly into the network output. Unlike the distributed PINN (DPINN) strategy of Ref.~\cite{Li2023}, which partitions the radial domain into subdomains with separate networks, we employ a \emph{unified} fully connected network over the entire interval $[r_{\min},r_{\max}]$, avoiding spurious jumps at subdomain interfaces. Moreover, whereas Ref.~\cite{Li2023} restricts training to $r\in(10,300)$---well outside the steep $1/r$ and $1/r^2$ curvature of the inner exterior---we begin at $r_{\min}=10^{-2}M$, spanning three decades in radius and covering the strongly varying region that DPINNs sidestep by domain truncation. Holding the mass fixed at $M=1$, we sweep electric charge $Q\in\{0,0.5,1.0,1.1\}$ at $Λ=0$ and sweep $Λ\in\{0,0.1,-0.1\}$ at $Q=0.5$. All configurations achieve relative $\mathcal{L}_2$ errors below $6\%$ against the analytic reference. For the representative case $Q=0.5$, $Λ=0.1$, three independent trainings with fixed seeds yield relative errors of $3.89\%$, $1.08\%$, and $2.76\%$ (mean $2.58\%$, standard deviation $1.41\%$), demonstrating robustness of the mesh-free approach without labeled field data.
Source: arXiv (Cornell University)
Authors: Jin, Huan, Wu, Fei, Xue, Fei
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214588971