Geodetic precession is an effect predicted by General Relativity. In pulsar binary systems it predicts that the spin axis precesses around the rotation axis due to a gravitational spin-orbit coupling, in cases where the spin axis is misaligned with the orbital angular momentum vector. The inclination of the pulsed radiation respect to our line-of-sight changes and, as a consequence, the observed pulse profile also change. This feature can be identified from observation of radiadition properties if the system is tight enough. The angular rate of precession is given by: $$ \Omega_{geod} = \left( \frac{2\pi}{P_b} \right)^{5/3}T_\odot^{2/3}m_c \frac{4m_p + 3m_c}{2(m_p + m_c)^{4/3}}\frac{1}{1-e²}, $$ where \( T_\odot = GM_\odot /c^3 ~~\mu s\). Consequently, pulsar beams are not always pointing to the same direction, and for those higly relativistic the pulse can desapear from our field of view within a few years. This is the case of the Hulse-Taylor pulsar (PSR B1913+16), that will probably move out of our line-of-sight around the year 2025.

Pulsars and NSs are born from the core collapse of massive stars. Asymmetries in the supernova explosion are believed to imparth birth kicks on the newly-born NS, which can misaligne the spin vector depending on its magnitude. In binary systems, if both components remains bound after the first explosion, the further evolution, involving a mass transfer phase, will depend on the mass of the companion star. If it has a low mass, angular momentum exchange and tidal interactions will occur in slow timescales, enough for the vectors to align. On the other side, if the companion is sufficiently massive to undergo a second supernova explosion, the timescale will be shorter and a kick may be imparted on the newly born NS, tilting the orbit respect to the pre-SN configuration. The spin vector of the first born NS will be misaligned with the total angular momentum after the supernova, causing it to precess. The misalignment angle ( \( \delta \)) can be calculated as $$ \delta = \tan^{-1} \left( \frac{\omega \sin{\theta} \sin{\phi }}{\sqrt{(v_{rel} + \omega \cos{\theta })^2} + (\omega \sin{\theta } \cos{\phi }) ^2} \right), $$ where \( \omega \) is the kick velocity magnitude, \( \theta \) and \( \phi \) are kick angles and \( v_{rel}\) is the relative velocity between the two stars before the explosion.

The standard scenario of DNS formation predicts that after the first supernova the system evolves through a common envelope phase during the giant phase of companion star. The NS, embbeded in the companion envelope, inspiral close to the core of the companion and drag forces help to expel the envolpe. A second mass transfer (case BB RLO) might take place at this point and an accretion torque will tend to align the spin of the NS with the orbital angular momentum. At the onset of secondary supernova explosion a kick will be imparted at the second NS changing the angular momentum vector, so that the spin of first SN will be misaligned. It is important to note, however, taht the amount of ejected matter will be much lower compared to the first SN, and hence the imparted kick will be smaller.