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Dynamic behavior of time space holes.

Posted 9 days ago
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I want to compute the dynamic behavior of holes in spacetime, probably by using the finite element method. Given a smooth, closed surface, I want to compute the evolution of the surface from the given initial shape to its final, spherical shape. Astrophysics holds that holes exhibit practically no dynamic behavior and I want prove the general relativity says they do exhibit wonderful behavior.

Given a smooth, closed surface, I need:

An automatic 3D mesh generator for the exterior of the surface.

To solve for the minimum curvature gravity field that has zero radius of curvature on the surface and zero curvature on the boundary of the computational domain. Assuming an initially stationary spacetime completes the definition of the initial conditions.

Solve Einstein's field equations to simulate the evolution of the field by itself under general relativity. Spacetime is an elastic substance with mass, momentum, and a reference state that is completely flat. As the field tries to reach minimum curvature, the hole will ring and the field will radiate gravity waves making the hole more spherical.

Reconstruct the surface from the interior boundary elements at each time step to render it for displays. Also for each time step, output the area of the surface and the mass of the field. I conjecture the two are proportional.

Does Mathematica have finite element simulation and mesh generators? What do you think of the idea.

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