How Can Numerical Solutions to General Relativity Enhance Computational Physics?

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Numerical solutions to General Relativity (GR) are indeed a significant aspect of computational physics, particularly through methods like Regge Calculus, which involves discretizing spacetime into triangular surfaces. This approach allows for the representation of the metric and Riemann tensor in a finite framework, facilitating the quantization process. The challenge lies in defining essential quantities such as the metric tensor g_{ab} and the Riemann tensor R_{ab} within this discrete structure. Users express difficulty in understanding how to recover the Riemann tensor from these finite representations. Overall, the discussion highlights the complexities and potential of applying numerical methods to GR in computational physics.
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Hello could someone give some info about the "Numerical solution" to GR...is this a field of "Computational Physics"?..

- What i know is that you take the Hyper-surface, and you " split " it into triangles..and use the ¿angles? of every triangle as finite-coordinates..then you get a problem with finite degrees of freedom...but What happens with the metric, Riemann Tensor Energy-momentum tensor in this discrete space-time?..could you use discrete espace but continuous time so the usual Einstein Lagrangian becomes a finite one in the form:

L(q_i ,\dot q_i ,t) so it's easier to "Quantize" than the continuous one?..

- Main questions: how do you define g_{ab} R_{ab} and other quantities into a finite "triangularized" surface..thanks :rolleyes: :rolleyes:
 
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Look up "Regge Calculus".
 
robphy said:
Look up "Regge Calculus".

I was afraid of this answer... :cry: :cry: i have looked it up in "Wikipedia" and "Arxiv.org" but i don't see or can't understand the explanation...or how you recover the Riemann Tensor in the end...
 
MOVING CLOCKS In this section, we show that clocks moving at high speeds run slowly. We construct a clock, called a light clock, using a stick of proper lenght ##L_0##, and two mirrors. The two mirrors face each other, and a pulse of light bounces back and forth betweem them. Each time the light pulse strikes one of the mirrors, say the lower mirror, the clock is said to tick. Between successive ticks the light pulse travels a distance ##2L_0## in the proper reference of frame of the clock...

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