Hyperboloidal Initial Data with Prescribed Asymptotic Charges

Abstract

A novel method is introduced for constructing hyperboloidal initial data with direct analytic control over asymptotic charges prior to solving the Einstein constraint equations. Using the parabolic-hyperbolic formulation of the constraints together with a Fuchsian-analysis-inspired spectral solver, the asymptotic degrees of freedom, which determine infinite towers of asymptotic charges, including the Bondi energy and angular momentum, are used to prescribe the asymptotic behavior of solutions. As a proof of concept, we explicitly construct hyperboloidal initial data for a spinning black hole with Bondi energy $E_B = 2$ and angular momentum $J_B = 1/2$, starting from seed data induced on a hyperboloidal slice of the non-rotating Schwarzschild spacetime with mass $M=1$.