5 papers
Orthogonal Geodesic Chords, Brake Orbits and Homoclinic Orbits in Riemannian Manifolds
Roberto Giambó, Fabio Giannoni, Paolo Piccione
The study of solutions with fixed energy of certain classes of Lagrangian (or Hamiltonian) systems is reduced, via the classical Maupertuis--Jacobi variational principle, to the st…
Comment on "Spherically symmetric perfect fluid in area-radial coordinates" by Iguchi et al
Roberto Giambo', Fabio Giannoni, Giulio Magli +1
In this short note we comment about some criticisms - appeared in a recent paper by Iguchi et al - to our previous works on gravitational collapse of perfect fluids. We show that t…
A Generalized Index Theorem for Morse-Sturm Systems and Applications to semi-Riemannian Geometry
F. Giannoni, A. Masiello, P. Piccione +1
We prove an extension of the Index Theorem for Morse-Sturm systems of the form , where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus…
The Fermat Principle in General Relativity and Applications
Fabio Giannoni, Antonio Masiello, Paolo Piccione
In this paper we use a general version of Fermat's principle for light rays in General Relativity and a curve shortening method to write the Morse relations for light rays joining…
Morse Theory for the Travel Time Brachistochrones in Stationary Spacetimes
Fabio Giannoni, Paolo Piccione, Daniel V. Tausk
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…