The impact of the spin–orbit misalignment and of the spin of B on the Lense–Thirring orbital precessions of the double pulsar PSR J0737–3039A/B

In the Double Pulsar, Lense-Thirring periastron precession $\dot\omega^\mathrm{LT}$ should be measured by end of this decade. The analyses recently appeared in literature rely upon a formula for $\dot\omega^\mathrm{LT,\,A}$ induced spin angular momentum ${\boldsymbol{S}}^\mathrm{A}$ A valid if orbital $\boldsymbol{L}$ and are aligned, neglecting $\dot\omega^\mathrm{LT,\,B}$ because smallness ${\boldsymbol{S}}^\mathrm{B}$. impact on departures ${\boldsymbol{S}}^\mathrm{A}$-$\boldsymbol{L}$ geometry from ideal alignment is calculated. With current upper bound misalignment angle $\delta_\mathrm{A}$ between them, angles $\lambda_\mathrm{A},\,\eta_\mathrm{A}$ constrained within $85^\circ \lesssim \lambda_\mathrm{A}\lesssim 92^\circ,\, 266^\circ \eta_\mathrm{A} 274^\circ$. units $\dot\omega^\mathrm{GR}=16.89^\circ\,\mathrm{yr}^{-1}$, range variation as little $\Delta\dot\omega^\mathrm{LT,\,A}\doteq\dot\omega^\mathrm{LT,\,A}_\mathrm{max} - \dot\omega^\mathrm{LT,\,A}_\mathrm{min} = 8\times 10^{-8}\,\omega^\mathrm{GR}$ implied. experimental uncertainty $\sigma_{\dot\omega_\mathrm{obs}}$ measuring rate with SKA 1-mid telescope become smaller 2028-2030. Then, spatial orientation ${\boldsymbol{S}}^\mathrm{B}$ existing bounds $\delta_\mathrm{B}$, $\dot\omega^\mathrm{LT,\,B}\simeq 2\times 10^{-7}\,\dot\omega^\mathrm{GR}$ correspondingly error at transition MeerKAT+ facility to around 2025. (Abridged)