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Contents
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.
GENERAL RELATIVITYThus, 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
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.
Differential ManifoldsIntroduction 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.
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