12 citations · 60 across the 17 of their papers we have counts for
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Globally maximal timelike geodesics in static spherically symmetric spacetimes: radial geodesics in static spacetimes and arbitrary geodesic curves in ultrastatic spacetimes
Leszek M. Sokolowski, Zdzislaw A. Golda
This work deals with intersection points: conjugate points and cut points, of timelike geodesics emanating from a common initial point in special spacetimes. The paper contains thr…
First integrals in the Brans-Dicke cosmology
Zdzislaw A. Golda, Andrzej Woszczyna, Lukasz Bratek
The work presents the frst and the second degree Darboux polynomials, Jacobi's last multipliers as well as the set of frst integrals for Brans-Dicke cosmology. Algebraic invariant…
Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius
Leszek M. Sokołowski, Zdzislaw A. Golda
We refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti--de Sitter space in the ambient flat space. We prove that ea…
The local and global geometrical aspects of the twin paradox in static spacetimes: II. Reissner--Nordström and ultrastatic metrics
Leszek M. Sokołowski, Zdzisław A. Golda
This is a consecutive paper on the timelike geodesic structure of static spherically symmetric spacetimes. First we show that for a stable circular orbit (if it exists) in any of t…
The local and global geometrical aspects of the twin paradox in static spacetimes: I. Three spherically symmetric spacetimes
Leszek M. Sokołowski, Zdzisław A. Golda
We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provid…
Jacobi fields, conjugate points and cut points on timelike geodesics in special spacetimes
Leszek M. Sokołowski, Zdzisław A. Golda
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics.…