Variational derivative of metric determinant

[Soham Bhattacharyya]

Hi,

I am trying to take the variational derivative of the square root of the negative metric determinant with respect to the contravariant metric. While in https://link.springer.com/book/10.1007%2F978-3-319-18335-0, Page 701, Eq. (30), the overall sign in the variational derivative with respect to the contravariant metric is negative, the same with the VarD command is turning out to be positive.

I have attached the example with this message. Hope to hear from you soon.

Best regards,

Soham

[Jose]

Hi,

I think you are just missing a simplification taking into account that the determinant is negative:

Cheers,

Jose.

[Soham Bhattacharyya]

Hi Jose,

Thank you for your reply.

I was wondering if you ever thought of conducting a hackathon on xAct. Could be useful in coming up with new ways of using the engine.

With best regards,

Soham

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[Jose]

Hi Soham,

I never thought of doing something like that. We can organize some sort of xAct-related virtual meeting, and discuss suggestions and proposals. We can also do that in this forum too, which leaves a record for others to explore and refer to, even if it means a slower process.

Let us open a new thread and discuss possibilities.

Thanks,

Jose.