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July  2002, 8(3): 697-724. doi: 10.3934/dcds.2002.8.697

Morse theory for the travel time brachistochrones in stationary spacetimes

Fabio Giannoni 1, , Paolo Piccione 2, and  Daniel V. Tausk 2,

1. 

Dipartimento di Matematica e Fisica, Universitá di Camerino, Italy
2. 

Departamento de Matemática, Universidade de São Paulo, Brazil, Brazil

Received  January 2001 Revised  November 2001 Published  April 2002

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..
Mathematics Subject Classification: 58E05, 53C22, 83Cx.
Citation: Fabio Giannoni, Paolo Piccione, Daniel V. Tausk. Morse theory for the travel time brachistochrones in stationary spacetimes. Discrete & Continuous Dynamical Systems, 2002, 8 (3) : 697-724. doi: 10.3934/dcds.2002.8.697
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