Morse theory for the travel time brachistochrones in stationary spacetimes

Fabio Giannoni; Paolo Piccione; Daniel V. Tausk

doi:10.3934/dcds.2002.8.697

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2002, Volume 8, Issue 3: 697-724. Doi: 10.3934/dcds.2002.8.697

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Morse theory for the travel time brachistochrones in stationary spacetimes

1.
Dipartimento di Matematica e Fisica, Universitá di Camerino
2.
Departamento de Matemática, Universidade de São Paulo

Received: January 2001

Revised: November 2001

Published: July 2002

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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.

Mathematics Subject Classification: 58E05, 53C22, 83Cxx.

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