Morse theory for the travel time brachistochrones in stationary spacetimes

Pages: 697 - 724, Volume 8, Issue 3, July 2002

doi:10.3934/dcds.2002.8.697       Abstract        Full Text (336.0K)       Related Articles

Fabio Giannoni - Dipartimento di Matematica e Fisica, Universitá di Camerino, Italy (email)
Paolo Piccione - Departamento de Matemática, Universidade de São Paulo, Brazil (email)
Daniel V. Tausk - Departamento de Matemática, Universidade de São Paulo, Brazil (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.
Mathematics Subject Classification:  58E05, 53C22, 83Cxx.

Received: January 2001;      Revised: November 2001;      Published: April 2002.