MODELING GEODESIC LINES IN CURVED SPACETIME USING DIFFERENTIAL GEOMETRY WITHIN THE FRAMEWORK OF GENERAL RELATIVITY
Ключевые слова:
Differential geometry, general relativity, geodesics, curved spacetime, riemannian manifold, christoffel symbols, schwarzschild metric, lorentzian geometryАннотация
This paper investigates the modeling of geodesic lines in curved
spacetime using methods of differential geometry as applied within the framework of
General Relativity. By employing Riemannian geometry, we describe how free-falling
particles move along geodesics under gravitational influence, and how spacetime
curvature governs such motion. The study focuses on the mathematical structure of
Lorentzian manifolds, the computation of Christoffel symbols, and the formulation of
geodesic equations in Schwarzschild and Friedmann–Lemaître–Robertson–Walker
(FLRW) metrics. Symbolic computations were performed to derive geodesic trajectories
and analyze curvature effects. The outcomes demonstrate the effectiveness of differential
geometry in visualizing gravitational dynamics and deepen the mathematical understanding of Einstein’s field equations. These results can support both theoretical
research and computational physics education.
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