PreprintCC BY 4.0arXiv
Nonlinear Response of Schwarzschild Black Holes at Arbitrary Perturbative Order
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.
Related
- Weakly nonlinear strong-field signatures of spontaneously vectorized Einstein-vector-Gauss-Bonnet black holes near the Schwarzschild bifurcation
- Nonlinear stability of Schwarzschild black holes for the Einstein-massless Dirac system in spherical symmetry
- Second-order scattering response of a Schwarzschild black hole
- Second-order multipole response of two nearby incoherent sources in wave-optical imaging of a Schwarzschild black hole
- Perturbative solutions for the bumblebee field in a Schwarzschild background
BibTeX
@misc{chen2026nonlinear,
title = {{Nonlinear Response of Schwarzschild Black Holes at Arbitrary Perturbative Order}},
author = {Jiaqi Chen and Yu-Cun Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27048},
eprint = {2610.27048},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27048},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonlinear Response of Schwarzschild Black Holes at Arbitrary Perturbative Order
AU - Jiaqi Chen
AU - Yu-Cun Xie
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.27048
UR - https://arxiv.org/abs/2610.27048
AB - 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.
ER -