In static spherical spacetimes, the constant-speed brachistochrone is a geodesic of the Fermat optical metric, giving analytic fastest paths in the isothermal sphere and bent or straight paths in the Plummer galaxy.
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The brachistochrone problem for a constant velocity traveler in static and spherically symmetric spacetimes
In static spherical spacetimes, the constant-speed brachistochrone is a geodesic of the Fermat optical metric, giving analytic fastest paths in the isothermal sphere and bent or straight paths in the Plummer galaxy.