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

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

2012-03-04

arxiv.org/abs/1203.0748v1

Gen. Relativ. Gravit. (2012) 44:1267-1283

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, paper accepted for publication in Gen. Rel. Grav

Scientific paper

10.1007/s10714-012-1337-4

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 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.

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