Questions tagged [vector-fields]

Vector-fields are vector valued functions which define a vector at each point in space. Examples of the vector field include the electric field and the velocity of a fluid.

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Killing Tensor of Friedman-Robertson-Walker Metric

I would like help showing that the tensor, $$K_{\mu\nu}=a^2(g_{\mu\nu}+u_\mu u_\nu),$$ where $u^\mu =(1,0,0,0)$, is a Killing tensor of the spatially flat FRW metric, $$ds^2=-dt^2+a(t)^2\left(dr^2+d\...