Time-domain framework for the Teukolsky equation with a particle source using comoving hyperboloidal coordinates

arXiv:2606.26339 · gr-qc, astro-ph.HE · Submitted 2026-06-24 · Read on arXiv

Aditya Vaswani, Leor Barack, Oliver Long, Rodrigo Panosso Macedo

gr-qc, astro-ph.HE

Submitted: 2026-06-24

Comments: 18 pages, 12 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Initial Data — 11× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Benchmarking — 2× in this paper · explained in 3 episodes
• Abundance — 1× in this paper · explained in 1 episode
• Adaptation — 1× in this paper · explained in 1 episode
• Calibration — 1× in this paper · explained in 7 episodes
• Generalization — 1× in this paper · explained in 13 episodes

Sources

• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• Frequency-domain approach to self-force in hyperbolic scattering
• Frequency-domain self-force calculations using Gegenbauer reconstruction
• Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory
• Time-domain metric reconstruction for hyperbolic scattering
• Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
• Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
• Radiation outer boundary conditions and near-to-far field signal transformations for the Bardeen-Press equation
• Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
• Numerical solution of the 2+1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late-time decays
• Axisymmetric fully spectral code for hyperbolic equations
• Numerical investigation of the dynamics of linear spin $s$ fields on Kerr background I. Late time tails of spin $s = \pm 1, \pm 2$ fields
• Numerical investigation of the dynamics of linear spin $s$ fields on a Kerr background II: Superradiant scattering
• A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime
• Discontinuous collocation and symmetric integration methods for distributionally-sourced hyperboloidal partial differential equations
• Hyperboloidal discontinuous time-symmetric numerical algorithm with higher order jumps for gravitational self-force computations in the time domain
• Toward exponentially-convergent simulations of extreme-mass-ratio inspirals: A time-domain solver for the scalar Teukolsky equation with singular source terms

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