The theory of Schwarzschild timelike geodesics is revisited. Basing on a result by Weierstrass and Biermann, we derive a formula describing all non radial, time-like trajectories in terms of Weierstrass elliptic functions. Quite... more
The theory of Schwarzschild timelike geodesics is revisited. Basing on a result by Weierstrass and Biermann, we derive a formula describing all non radial, time-like trajectories in terms of Weierstrass elliptic functions. Quite remarkably, a single formula works for an entire geodesic trajectory, even if it passes through turning points. Using this formula, we derive expressions for the proper and coordinate time along the geodesic.
Научная биография Карла Вейерштрасса, его основные работы, влияние его учения на развитие математики. Karl Weierstrass bicentenary, scientific biography, major works, the significance of his teachings for mathematics.
We investigate certain properties of su(N)-valued two-dimensional soliton surfaces associated with the integrable CP^{N −1} sigma models constructed by the orthogonal rank-one Hermitian projectors , which are defined on the... more
We investigate certain properties of su(N)-valued two-dimensional soliton surfaces associated with the integrable CP^{N −1} sigma models constructed by the orthogonal rank-one Hermitian projectors , which are defined on the two-dimensional Riemann sphere with finite action functional. Several new properties of the projectors mapping onto one-dimensional subspaces as well as their relations with three mutually different immersion formulas , namely , the generalized Weierstrass , Sym-Tafel and Fokas-Gel ' fand have been discussed in detail. Explicit connections among these three surfaces are also established by purely analytical descriptions and , it is demonstrated that the three immersion formulas actually correspond to the single surface parametrized by some specific conditions .
