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unih
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Does anybody knows the package that can, given metric and equation of hypersurface (spacelike or null )calculate induced metric, external curvature and expansion (Raychaudhuri equation) in Mathematica.
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Geodesic expansion in Mathematica is a method for computing the geodesic equation, which describes the shortest path between two points on a curved surface. It allows for the calculation of geodesic distances and curves on a variety of surfaces, including spheres, ellipsoids, and more complex surfaces.
Geodesic expansion in Mathematica works by using the built-in functions of the software to create a parametric form of the surface and then using the geodesic equation to calculate the shortest path between two points on that surface. It uses a combination of numerical and symbolic calculations to accurately compute the geodesic distances and curves.
Using geodesic expansion in Mathematica allows for accurate and efficient computation of geodesic distances and curves on a variety of surfaces. It also provides a visual representation of these calculations, making it easier to understand and interpret the results. Additionally, Mathematica's built-in functions and capabilities make it a powerful tool for performing complex calculations.
Yes, geodesic expansion in Mathematica can be applied to real-world problems in various fields such as physics, engineering, and mathematics. It can be used to analyze and optimize routes for transportation, map out optimal paths for robots or drones, and calculate the shortest distance between two points on a curved surface.
While geodesic expansion in Mathematica is a powerful tool, it does have some limitations. It may not be suitable for extremely complex surfaces or situations where numerical errors can significantly affect the results. Additionally, it may require some understanding of Mathematica syntax and functions to use effectively.