Abstract

We obtain some results in both Lorentz and Finsler geometries, by using a correspondence between the conformal structure (Causality) of standard stationary spacetimes on M = R x S and Randers metrics on S. In particular: (1) For stationary spacetimes: we give a simple characterization of when R x S is causally continuous or globally hyperbolic (including in the latter case, when S is a Cauchy hypersurface), in terms of an associated Randers metric. Consequences for the computability of Cauchy developments are also derived. (2) For Finsler geometry: Causality suggests that the role of completeness in many results of Riemannian Geometry (geodesic connectedness by minimizing geodesics, Bonnet-Myers, Synge theorems) is played by the compactness of symmetrized closed balls in Finslerian Geometry. Moreover, under this condition we show that for any Randers metric R there exists another Randers metric R with the same pregeodesics and geodesically complete. Even more, results on the differentiability of Cauchy horizons in spacetimes yield consequences for the differentiability of the Randers distance to a subset, and vice versa.

Autore Pugliese

• Caponio Erasmo

Tutti gli autori

• Caponio E , Javaloyes MA , Sanchez M

Titolo volume/Rivista

REVISTA MATEMATICA IBEROAMERICANA

Anno di pubblicazione

2011

ISSN

0213-2230

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

30

Ultimo Aggiornamento Citazioni

2017-04-23 03:20:56

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile