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{{\left( {{\xi }_{\nu }}{{T}^{\mu }}^{\nu } \right)}_{\mathrm{;}}}_{\mu }=\underbrace{{{\xi }_{\nu }}{{_{\mathrm{;}}}_{\mu }}{{T}^{\mu }}^{\nu }}_{=0}+\underbrace{{{\xi }_{\nu }}{{T}^{\mu }}{{^{\nu }}_{\mathrm{;}}}_{\mu }}_{=0}=0

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(ξνTμν);μ=ξν;μTμν=0+ξνTμν;μ=0=0
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