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A comment on "Lense-Thirring frame dragging induced by a fast-rotating white dwarf in a binary pulsar system" by V. Venkatraman Krishnan et al

We comment on a recent study reporting evidence for the general relativistic Lense-Thirring secular precession of the inclination $I$ of the orbital plane to the plane of the sky of the tight binary system PSR J1141-6545 made of a white dwarf and an emitting radiopulsar of comparable masses. The quadrupole mass moment $Q_2^\mathrm{c}$ and the angular momentum ${\boldsymbol S}^\mathrm{c}$ of the white dwarf cause the detectable effects on $I$ with respect to the present-day accuracy in the pulsar's timing. The history-dependent and model-dependent assumptions to be made on $Q_2^\mathrm{c}$ and ${\boldsymbol S}^\mathrm{c}$, required even just to calculate the analytical expressions for the resulting post-Keplerian precessions, may be deemed as too wide in order to claim a successful test of the Einsteinian gravitomagnetic effect. Moreover, depending on how $Q_2^\mathrm{c}$ is calculated, the competing quadrupole-induced rate of change, which is a major source of systematic uncertainty, may be up to $\lesssim 30-50\%$ of the Lense-Thirring effect for most of the allowed values in the 3D parameter space spanned by the white dwarf's spin period $P_\mathrm{s}$, and the polar angles $i_\mathrm{c},\,ζ_\mathrm{c}$ of its spin axis. The possible use of the longitude of periastron $\dot\varpi$ is investigated as well. It turns out that a measurement of its secular precession, caused, among other things, also by $Q_2^\mathrm{c},\,{\boldsymbol{S}}^\mathrm{c}$, could help in further restricting the permitted regions in the white dwarf's parameter space.