The paper introduces brachistochrone-ruled timelike surfaces in Newtonian and relativistic spacetimes, with rulings as time-minimizing trajectories, and gives explicit constructions in Minkowski spacetime (straight lines, totally geodesic surfaces) and Schwarzschild spacetime (via Jacobi metrics and
F., Bender, C.M., 1986, J
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Brachistochrone-ruled timelike surfaces in Newtonian and relativistic spacetimes
The paper introduces brachistochrone-ruled timelike surfaces in Newtonian and relativistic spacetimes, with rulings as time-minimizing trajectories, and gives explicit constructions in Minkowski spacetime (straight lines, totally geodesic surfaces) and Schwarzschild spacetime (via Jacobi metrics and