Coupled metric-scalar perturbations in dynamical Chern-Simons gravity

Develop a full treatment of the coupled metric and scalar perturbation equations for gravitational waves from pulsar glitches in dynamical Chern-Simons gravity, including dynamical scalar perturbations beyond the leading background-scalar approximation.

Background

The analysis neglects dynamical scalar perturbations δϑ\delta\vartheta and retains only the birefringent effect generated by the stationary dipolar scalar field sourced by the rotating neutron star. This approximation is used to derive a single modified Regge–Wheeler equation for the axial gravitational perturbation.

A complete treatment would require solving the coupled metric-scalar perturbation system rather than treating the scalar perturbation as subleading. Such a calculation could determine whether additional scalar dynamics modify the predicted birefringent effect at higher order in the Chern-Simons coupling.

References

A full treatment would require solving the coupled metric-scalar perturbation equations, which we leave for future work.

— Gravitational Wave Parity-Violating Strain from Pulsar Glitches in Chern-Simons Modified Gravity  (2608.24002 - Rout et al., 25 Aug 2026) in Section 6.5, “Limitations and Caveats”; also Appendix C, Section “Cotton Tensor and Its Perturbation”