Half-angle boost aberration of a null spinor ($\tan ({\theta }^{\prime }/2)=e^{-\kappa }\tan (\theta /2)$)

The spinor boost $\mathrm{diag}(e^{\kappa /2},e^{-\kappa /2})$ changes the component-magnitude ratio by $e^{-\kappa }$. The associated active positive-$z$ Lorentz boost therefore changes the polar half-angle as displayed and leaves azimuth unchanged. Its null-vector time scale changes by $\cosh \kappa +\sinh \kappa \cos \theta$, which must be retained separately when normalizing a spinor to encode direction.