VarD in case of 3+1 decomposition

[Pawan Kumar Gupta]

Hi,

I am trying to compute the Variational derivative for Lagrangian L which has variable defined on 3dim manifold and time derivate is defined as ParamD[t]. To compute Variational Derivative,

  VarD[\[Phi][],CD][L] where CD is covariant derivative on 3dim manifold

Clearly, this won't give the correct variation of L, because time variation in missing. But adding VarD of time also does not give correct result.

VarD[\[Phi][],CD][L]  + VarD[\[Phi][],ParamD[t]][L]

So, I was wondering how to do VarD correctly in this case ?

Thank you in Advance!

[Jose]

Hi,

This is a good point. I had never thought of this case, and I'm afraid VarD does not handle it at the moment. xTensor implicitly assumes that you will first take variations and then perform a 3+1 decomposition, rather than viceversa.

We should find a way of extending VarD to use several derivatives simultaneously.

Thanks for the suggestion,

Jose.