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Question: Re: :Why is the sign incorrect when I differentiate a covariant metric with respect to a contravariant metric, or vice versa?

Question:Re: :Why is the sign incorrect when I differentiate a covariant metric with respect to a contravariant metric, or vice versa?

struckmeier 70 Maple
physics
March 02 2019
1

The sign error calculating the derivative of a contravariant metric with respect to the covariant metric as diff(g_[`~nu`, `~tau`], g_[mu, eta]) and vice versa based on the Physics package is meanwhile resolved if you install the lastes update version 315.

However, a similar error occurs with the Tetrad package. If one calculates

diff(e_[~a, mu], e_[b, ~nu])

the obtained result is

eta_[~a, ~b] * g_[mu, nu].

But the is wrong! The correct result is

-e_[~a,nu] * e_[~b,mu].
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