Abstract

In this paper, we first study some global properties of the energy functional on a non-reversible Finsler manifold. In particular we present a fully detailed proof of the Palais--Smale condition under the completeness of the Finsler metric. Moreover we define a Finsler metric of Randers type, which we call Fermat metric, associated to a conformally standard stationary spacetime. We shall study the influence of the Fermat metric on the causal properties of the spacetime, mainly the global hyperbolicity. Moreover we study the relations between the energy functional of the Fermat metric and the Fermat principle for the light rays in the spacetime. This allows one to obtain existence and multiplicity results for light rays, using the Finsler theory. Finally the case of timelike geodesics with fixed energy is considered. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM

Autore Pugliese

• Caponio Erasmo , Masiello Antonio

Tutti gli autori

• Caponio E , Javaloyes MA , Masiello A

Titolo volume/Rivista

MATHEMATISCHE ANNALEN

Anno di pubblicazione

2011

ISSN

0025-5831

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

31

Ultimo Aggiornamento Citazioni

2017-04-23 03:20:56

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile