On the occurrence of Closed Timelike Curves and the observer’s point of view

¹ Istituto per le Applicazioni del Calcolo “M. Picone,” CNR, I-00185 Rome, Italy
² ICRA, University of Rome “La Sapienza,” I-00185 Rome, Italy
³ INFN, Sezione di Firenze, I–00185 Sesto Fiorentino (FI), Italy
⁴ INAF, Astronomical Observatory of Torino, I–10025 Pino Torinese (TO), Italy
⁵ Physics Department, University of Rome “La Sapienza,” I-00185 Rome, Italy

^a e-mail: binid@icra.it
^b e-mail: geralico@icra.it

Published online: 5 September 2013

Abstract

The existence of Closed Timelike Curves (CTCs) in a generic spacetime is often associated with a non-physical choice of coordinates and can be cured by limiting the admissibility of such coordinates. Lichnerowicz conditions, for instance, represent a criterion for admissibility. The result, however, is a very restrictive limitation which may imply “removal” of important regions (with respect to the peculiarity of phenomena which may happen there) of the spacetime manifold. We consider here the point of view of a family of observers (Fundamental Slicing Observers, FSO) having their world lines orthogonal to the surfaces of constant coordinate time. We say that the time coordinate has not a global character if the associated FSO change their causality condition in the domain of validity of the coordinates themselves. Furthermore, in those regions where FSO have no more timelike world lines, CTCs are present and one may think of special devices or investigation tools apt to operationally detect them. We will discuss in detail theoretical approaches involving (scalar) waves or photons.