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Morse theory for the travel time brachistochrones in stationary spacetimes

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  • The travel time brachistochrone curves in a general relativistic framework are timelike curves, satisfying a suitable conservation law with respect to a an observer field, that are stationary points of the travel time functional. We develop a global variational theory for brachistochrones joining an event p and the worldline of an observer $\gamma$ in a stationary spacetime $\mathcal M$.
    Mathematics Subject Classification: 58E05, 53C22, 83Cxx.


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