How Can Numerical Solutions to General Relativity Enhance 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...
 
From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
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