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Bogoliubov quasiparticles moving in the background of superfluid$\text{He}^3$-A see an apparently curved space-time metric when the backgroundsuperfluid vacuum is in motion. We study how this curvature couples with thespins of the effectively massless quasiparticles. First, we set up the problemin null Fermi coordinates for radial as well as circular geodesics and then useit in the context of the analog metric seen by the quasiparticles. We obtain aneffective magnetic interaction due to curvature coupling, and provide numericalestimates. Some possible implications of these results are then pointed out.

Massless fermions in null Fermi coordinates and an application to analog gravity in $\text{He}^3$-A