The Twin Paradox in Static Spacetimes and Jacobi Fields
The twin paradox of special relativity formulated in the geometrical setting of general relativity gives rise to the problem of determining the longest timelike curve between a given pair of points. As a first step one solves the local problem for a bundle of nearby curves (geodesics) in terms of Jacobi fields and conjugate points. These provide important information about geometrical properties of the given spacetime. The second step, to determine the globally maximal length curve in the set of all timelike curves with common endpoints, is harder and may be effectively performed only in spacetimes with high symmetries.
- 1.Abramowicz, M., Bajtlik, S., Kluźniak, W.: The twin paradox on the photon sphere. Phys. Rev. A 75, 044101 (2007). doi: 10.1103/PhysRevA.75.044101
- 2.Abramowicz, M., Bajtlik, S.: Adding to the paradox: the accelerated twin is older (2009). ArXiv e-prints 0905.2428[physics.class-ph]
- 4.Beem, J., Ehrlich, P., Easley, K.: Global Lorentzian Geometry. In: Monographs and Textbooks in Pure and Applied Mathematics, vol. 202, 2nd edn. Marcel Dekker, New York (1996)Google Scholar
- 5.Sokołowski, L. M., Golda, Z. A.: Jacobi fields, conjugate points and cut points on timelike geodesics in special spacetimes. ArXiv e-prints arxiv:1402.3976[gr-qc]Google Scholar