Locally inertial reference frames in Lorentzian and Riemann-Cartan spacetimes
Article first published online: 27 MAR 2012
Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 524, Issue 5, pages 302–310, May 2012
How to Cite
Giglio, J.F.T. and Rodrigues, W.A. (2012), Locally inertial reference frames in Lorentzian and Riemann-Cartan spacetimes. Ann. Phys., 524: 302–310. doi: 10.1002/andp.201100302
- Issue published online: 7 MAY 2012
- Article first published online: 27 MAR 2012
- Manuscript Accepted: 9 FEB 2012
- Manuscript Revised: 8 FEB 2012
- Manuscript Received: 11 NOV 2011
- Locally inertial reference frames;
- Lorentzian spacetimes;
- Riemann-Cartan spacetimes.
In this paper the concept of locally inertial reference frames (LIRFs) in Lorentzian and Riemann-Cartan spacetime structures is scrutinized. A rigorous mathematical definition of a LIRF in both structures is given, something that needs preliminary a clear mathematical distinction between the concepts of observers, reference frames, naturally adapted coordinate functions to a given reference frame and which properties may characterize an inertial reference frame (if any) in the Lorentzian and Riemann-Cartan structures. Hopefully, the paper clarifies some obscure issues associated to the concept of a LIRF appearing in the literature, in particular the relationship between LIRFs in Lorentzian and Riemann-Cartan spacetimes and Einstein's most happy thought, i.e., the equivalence principle.