Hi , im working with the following stress-energy tensor:(adsbygoogle = window.adsbygoogle || []).push({});

T_{[itex]\mu\nu[/itex]=}[itex]\partial[/itex]_{[itex]\mu[/itex]}[itex]\phi[/itex][itex]\partial[/itex]_{[itex]\nu[/itex]}[itex]\phi[/itex]^{*}- g^{[itex]\mu\nu[/itex]}([itex]\nabla[/itex]^{[itex]\mu[/itex]}[itex]\phi[/itex][itex]\nabla[/itex]_{[itex]\mu[/itex]}[itex]\phi[/itex]^{*}- m^{2}[itex]\phi\phi[/itex]^{*})

Where [itex]\phi[/itex] is a complex scalar of the form:

[itex]\phi[/itex](r,t) = [itex]\psi[/itex](r)e^{iwt}

that obeys the Klein-gordon equation and [itex]\phi[/itex]^{*}is the complex conjugate, and g the metric tensor.

My problem is that i think this tensor is not symmetric as T_{tr}/= T_{rt}by a minus sign on the term of the partial derivates.

Thanks a lot for reading.

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# Problems with a complex stress-energy tensor

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