A geometric multimessenger consistency test of radiative and near-zone gravity with LISA and SKA

Compact binary pulsars observed both through precision radio timing and low-frequency gravitational waves offer a direct way to compare the same binary geometry with two independent messengers. We propose a multimessenger consistency test based on the orbital inclination, measured from the Shapiro-delay shape parameter in radio timing and from the tensor polarization amplitude ratio in the gravitational-wave signal. Defining the common-epoch residual $\text{eps}(t_0)=s_{\mathrm{S}\mathrm{h}\mathrm{a}\mathrm{p}\mathrm{i}\mathrm{r}\mathrm{o}}(t_0)-s_{\mathrm{G}\mathrm{W}}(t_0)$, general relativity predicts $\text{eps}=0$, while a nonzero value would indicate either an unmodeled systematic or a mismatch between the near-zone and radiative descriptions of gravity. We estimate the attainable precision on this quantity for representative LISA–SKA compact binary pulsars using a seven-parameter timing Fisher matrix and a sky-averaged LISA sensitivity curve including the Galactic foreground. We adopt a conservative radio baseline, ${\sigma }_{\mathrm{T}\mathrm{O}\mathrm{A}}=1\mu \mathrm{s}$ and $N_{\mathrm{e}\mathrm{f}\mathrm{f}}={10}^4$, intended to summarize radiometer noise, jitter, residual dispersion-measure and scattering effects, profile evolution, and cadence losses after wideband timing. For systems at $d=5\mathrm{k}\mathrm{p}\mathrm{c}$ observed for four years, we find ${\sigma }_{\text{eps}}\simeq 4\times {10}^{-3}$ for a favorable double neutron star and ${\sigma }_{\text{eps}}\simeq 9\times {10}^{-4}$ for a hypothetical pulsar–black-hole system. The former is the more robust astrophysical benchmark; the latter illustrates the reach if such a high-SNR chirping source is discovered. The useful cases remain limited mainly by gravitational-wave polarimetry, while radio timing supplies the near-zone reference measurement of the inclination. These results define a quantitative target for future joint Bayesian analyses of compact binary pulsars observed in both radio and gravitational waves.