General Relativity and Gravitation

, Volume 44, Issue 5, pp 1267–1283 | Cite as

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

Open Access
Research Article

Abstract

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

Twin paradox Static spacetimes Jacobi fields Conjugate points 

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Astronomical ObservatoryJagiellonian UniversityKrakówPoland
  2. 2.Copernicus Center for Interdisciplinary StudiesKrakówPoland

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