Neural-Spectral Discovery of Rotating Black Holes Beyond General Relativity

Abstract

Finding rotating black hole solutions in higher-curvature theories of gravity is a problem of fundamental importance. Virtually every approach to reconcile gravity with quantum mechanics predicts corrections to the Einstein-Hilbert action, yet no systematic solution-generating method exists for the stationary sector. We close this gap with {\sc Akribeia}, a novel hybrid framework that pairs physics-informed neural networks with a pseudo-spectral refinement step, yielding certified neural-field rotating black hole solutions -- continuous, globally defined functions, parametric in the coupling constants -- whose residuals against the field equations are verified to extreme precision. We apply the method to theories quadratic and cubic in the curvature and construct, for the first time, families of rotating black holes featuring multiple non-vanishing angular momenta, parametric in the new coupling constants. After validating against previously known five-dimensional spacetimes, we present new solutions in scenarios leading to a highly non-linear/non-perturbative coupled system of ordinary differential equations. Our method can be systematically adapted to other setups involving partial differential equations as well.