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On the geometric nature of the twin paradox in curved spacetimes

Sokołowski L. M.

Demonstratio Mathematica

2017

Vol. 50, nr 1

56--65

The famous „twin paradox” of special relativity is of purely geometric nature and formulated in curved spacetimes of general relativity motivates investigations of the timelike geodesic structure of these manifolds. Except for the maximally symmetric spacetimes the search for the longest timelike curves is hard, complicated and requires both advanced methods of global Lorentzian geometry and solving the intricate geodesic deviation equation. This article is a theoretical introduction to the problem. First we describe the procedure of determining the locally longest curves; it is algorithmic in the sense of consisting of a small number of definite steps and is effective if the geodesic deviation equation may be solved. Then we discuss the problem of globally maximal timelike curves; due to its nonlocal nature there is no prescription of how to solve it in finite number of steps. In the case of sufficiently high symmetry of the manifold also the globally longest curves may be found. Finally we briefly present some results recently found.

The response of TEC at quasi-conjugate point GPS stations during solar flares

Bahari S.A., Abdullah M., Yatim B.

Acta Geophysica

2011

Vol. 59, no. 2

407-427

Global Positioning System (GPS) derived total electron content (TEC) measurements were analyzed to investigate the ionospheric response during the X-class solar flare event that occurred on 5-6 December 2006 at geomagnetic conjugate stations: Syowa, Antarctica (SYOG) (GC: 69.00° S, 39.58° E; CGM: 66.08° S, 71.65° E) and Árholt, Iceland (ARHO) (GC: 66.19° N, 342.89° E; CGM: 66.37° N, 71.48° E). Bernese GPS software was used to derive the TEC maps for both stations. The focus of this study is to determine the symmetry or asymmetry of TEC values which is an important parameter in the ionosphere at conjugate stations during these solar flare events. The results showed that during the first flares on 5 December, effects were more pronounced at SYOG than at ARHO. However, on 6 December, the TEC at ARHO showed a sudden spike during the flare with a different TEC variation at SYOG.

Conjugate points indefinite complex space forms

Erkekoglu F.

Demonstratio Mathematica

2006

Vol. 39, nr 3

643-648

The theorem below for the conjugate points in indefinite complex space forms is proven.