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Keep metric purely symbolic

asked 2023-06-23 14:03:08 +0200

Loreno Heer gravatar image

updated 2023-06-23 15:23:50 +0200

eric_g gravatar image

Is there an easy way to define a purely symbolic riemannian metric on a manifold? Or do I need to initialize it like this g[0,0] = function('g00')(t,x,y,z) for example?

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answered 2023-06-23 15:22:24 +0200

eric_g gravatar image

At the moment, all tensor fields on manifolds must have expressions in terms of coordinates in one or more charts, These expressions can involve some unspecified functions though, declared via function. So yes, the only way to define a generic metric is what you suggest. But in practice, for dimensions larger than 2 or 3, this can lead to untractable computations.

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oh, that is a pity. both in terms of writing it out and computationally. I will then use cadabra2 in the meantime for this.

Loreno Heer gravatar imageLoreno Heer ( 2023-06-23 15:52:37 +0200 )edit

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Asked: 2023-06-23 14:03:08 +0200

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Last updated: Jun 23 '23