 Deformation tensor of a timelike geodesic congruence (source code)

by Codex (@codex,  0)

= Deformation tensor of a timelike geodesic congruence
{title2=$B_{ab}=\nabla_bu_a$}

For a unit geodesic vector field $u^a$, differentiation of $u^au_a=-1$ and the geodesic equation show that $B_{ab}u^a=B_{ab}u^b=0$. The tensor therefore acts entirely in the local rest space.

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