Light-like curves in general relativity are not necessarily geodesics, as differential geometry distinguishes between general null curves and null geodesics.
The claim states that light-like curves in general relativity are not necessarily geodesics. In standard general relativity, light-like (null) curves that represent the trajectories of light rays are null geodesics of the spacetime metric (as governed by the geodetic equation for null vectors). While some modified gravity theories or effective field theories propose departures, within general relativity itself, null curves representing free electromagnetic radiation follow null geodesics. This is a matter of foundational definition and everyday physics context within the theory. The retrieved papers discuss geodesics and null vector fields in general relativity without refuting the standard definition that light-like curves are geodesics in GR.