Exact modified Teukolsky operator for spinning beyond-Einstein black holes

Determine the exact form of the modified Teukolsky operator for generically spinning black holes in theories with beyond-Einstein curvature couplings, enabling wave-generation calculations that are accurate to linear order in the coupling parameter.

Background

The paper models the gravitational-wave signal of an extreme-mass-ratio inspiral around a black hole carrying massive scalar hair induced by dynamical Chern–Simons or scalar Gauss–Bonnet curvature couplings. The authors account for the conservative deformation of the black-hole geometry and include scalar radiation, but they approximate the wave operator with its Kerr/general-relativistic counterpart rather than solving the fully modified perturbation problem.

The missing calculation is required to capture the coupling-dependent correction to gravitational-wave generation itself. The authors state that this correction is the only truncated component of the relevant O(eta zeta) dynamics and that the exact operator is not currently available for generically spinning black holes with beyond-Einstein couplings.

References

Since the exact modified Teukolsky operator for generically spinning BHs with beyond-Einstein couplings remains an open problem, this modified wave generation is the only piece we truncate.

— Devoured by a Hairy Gargantua: Probing Massive Scalar Charges with Non-minimal Curvature Coupling with Extreme-Mass-Ratio Inspirals  (2608.28037 - Lui et al., 28 Aug 2026) in Section 2, “Metric Perturbations and Transition-to-Plunge Trajectory Modified by Massive Scalar Charges”

We conjecture that including these corrections would not drastically alter our results and, if anything, could tighten the constraints on the scalar charge, making our forecast conservative.

— Devoured by a Hairy Gargantua: Probing Massive Scalar Charges with Non-minimal Curvature Coupling with Extreme-Mass-Ratio Inspirals  (2608.28037 - Lui et al., 28 Aug 2026) in Section 5, “Discussion and Conclusion”

During the subsequent plunge the motion becomes increasingly noncircular, and a controlled treatment would require the corresponding source-driven modified-Teukolsky calculation for generic trajectories, which is not presently available. As our baseline prescription, we therefore retain the full GR EOB radiation reaction through the transition and plunge while smoothly switching off only the unavailable beyond-GR flux corrections once the circular-orbit MTF input terminates.

— From the Test-Mass Limit to Binary Black-Hole Waveforms in Higher-Derivative Gravity  (2609.11726 - Yang et al., 10 Sep 2026) in Section 3, Subsection “Continuation through the plunge”