Following Wald I have nearly got the right answer out for time derivative for shear...what I am left with is showing that [itex]R_{cbad} V^c V^d + h_{ab} R_{cd} V^c V^d / 3[/itex] (which is obviously symmetric and trace-free) can be written as [itex]C_{cbad} V^c V^d + \tilde{R}_{ab} / 2[/itex] where [itex]\tilde{R}_{ab}[/itex] is the spatial, trace-free part of [itex]R_{ab}[/itex], i.e. [itex]h_{ac} h_{bd} R^{cd} - h_{ab} h_{cd} R^{cd} / 3[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Is there an easy way of proving this?

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# Raychaudhuri equation for shear

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