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GENERAL RELATIVITY

Mass bends the Space-Time around an object. An object has to follow the bending space and the path becomes curved. This holds even for fast moving objects like light rays. Thus, light rays have to follow the bending space. Even assuming a mass for light quants the classical mechanical theory predicts less curved paths of light rays in the vicinity of a massive object. So, gravitation is not a force effecting an object in a specific time. But rather effecting the object's path directly independent on the amount of time which the object spends on the path.

Thus, the observed acceleration, change of velocity and direction of the object's path, has to be viewed as a direct effect of Space-Time. The curvature is computed by the curvature of the Rieman Space-Time manifold.

Movements in Space-Time



The path of an object is describes by geodesic curves representing the 1. Law of Newton. The path is described by the so called separation ds dependent on the object's 4th dimensional position and it's first derivate (velocity) and the Metric Tensor.

Acceleration

Acceleration is the 2nd differential of the 4th dimensional Space-Time position. The acceleration caused by gravitation can be described as an effect of curvature in space.
Es gilt a= C^k_ij * dx^i * dx^j mit C : Christoffel Symbole und dx^i= aktuelle Geschwindigkeit

Differential Manifolds

Introduction to Differential Geometry and General Relativity

Simulations on General Relativity

Simulation der Gravitation (German) Some Notes on Problems with Numerical Simulations will give introduction how complicate it will get when simulating physical processes in detail.

The Simulation Contest The Orrey is an informal, bi-monthly newsletter whose main interest is computational astronomy. Another Simulation Home page

An interesting question is how something will look like if we view something under relativistic effects. Relativistic Ray Tracing will create images showing these effects.

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