On the twin paradox in static spacetimes : I. Schwarzschild metric

Bibliographic description

punktacja MNiSW [2012 A]: 30

title:	On the twin paradox in static spacetimes : I. Schwarzschild metric
author:	Sokołowski Lech
journal title:	General Relativity and Gravitation
volume:	44
issue:	5
date of publication :	2012
pages:	1267-1283
ISSN:	0001-7701
eISSN:	1572-9532
DOI:	10.1007/s10714-012-1337-4
language:	English
journal language:	English
abstract in English:	Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.
keywords in English:	twin paradox, static spacetimes, Jacobi fields, conjugate points
affiliation:	Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut – Obserwatorium Astronomiczne
type:	journal article
subtype:	academic paper