Powered by Indico
v3.2.7
Metric-affine gravity describes gravitational interactions within the most general spacetime where torsion, curvature, and non-metricity could all exist. Meanwhile, the concept of the autoparallel equation with a general affine connection has been proposed as a potential candidate for the trajectory motion of particles. In this work, we investigate whether the autoparallel equation can be derived as the trajectory motion for particles starting from a scalar-tensor theory action within metric-affine gravity. We show that neither the use of a general covariant derivative nor the inclusion of non-minimal couplings to torsion and non-metricity alters the resulting mass-shell condition. Consequently, the derived equation of motion does not yield the autoparallel equation. We formalize this finding into a no-go theorem: for general second-order scalar-tensor theories in metric-affine gravity, the autoparallel equation cannot be obtained from the scalar field derivation.