Morse theory for the travel time brachistochrones in stationary spacetimes
Fabio Giannoni - Dipartimento di Matematica e Fisica, Universitá di Camerino, Italy (email)
Abstract: 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 $\mathcal M$.
Keywords: Morse theory, variational theory.
Received: January 2001; Revised: November 2001; Published: April 2002.
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