Year: 2026
Type: preprint
Abstract: We establish recursive integration-by-parts identities that symbolically reduce the inhomogeneous solutions of the Regge-Wheeler-Zerilli equation to a small set of master integrals, yielding the nonlinear response kernels of Schwarzschild black holes at arbitrary perturbative order. We further derive a closed ODE system that enables rapid, accurate, and stable numerical evaluation of these master integrals. To demonstrate our result, we compute quadratic, cubic, and quartic quasinormal-mode coupling coefficients as special cases of the response kernels.
Source: arXiv (Cornell University)
Authors: Chen, Jiaqi, Xie, Yu-Cun
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, G2554637905, G2930580908, Category II: ACES - Accelerating Computing for Emerging Sciences, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4057808474, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G7113600513, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI, Collaborative Research: Testing General Relativity with Gravitational Wave Observations
OpenAlex ID: W7223124982